You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer must be formatted exactly as follows:
<think>
[your reasoning process here]
</think>
<answer>
[your answer here]
</answer>
You can choose to imitate the reasoning process of relevant algorithms or explore an appropriate solution on your own. DO NOT use code, and remember to focus on the logical flow.
system
Your task is to solve the Minimum Vertex Cover problem in the given social network. In this network, each node represents a user, and each edge represents a friendship connection. You need to identify the smallest subset of users such that every friendship connection has at least one user from this subset.

**Problem to Solve**

- Users in the network: Gavin Chavez, Andrew Dyer, Robert Smith, Nathaniel Bailey, Emily Simmons, Michelle Brown, Chase Anthony, Jeremy Franklin, Emily Wilkinson, Jennifer Peck, Kathryn Sanchez, Matthew Johnson, Paul Smith, Louis Carter, Monica Yang.
- Fiendship connections: Gavin Chavez and Monica Yang, Gavin Chavez and Kathryn Sanchez, Gavin Chavez and Paul Smith, Gavin Chavez and Louis Carter, Andrew Dyer and Kathryn Sanchez, Robert Smith and Kathryn Sanchez, Robert Smith and Paul Smith, Nathaniel Bailey and Kathryn Sanchez, Emily Simmons and Kathryn Sanchez, Michelle Brown and Kathryn Sanchez, Chase Anthony and Kathryn Sanchez, Chase Anthony and Paul Smith, Jeremy Franklin and Kathryn Sanchez, Jeremy Franklin and Paul Smith, Emily Wilkinson and Kathryn Sanchez, Emily Wilkinson and Paul Smith, Jennifer Peck and Kathryn Sanchez, Kathryn Sanchez and Monica Yang, Kathryn Sanchez and Paul Smith, Kathryn Sanchez and Louis Carter, Kathryn Sanchez and Matthew Johnson, Paul Smith and Monica Yang, Paul Smith and Louis Carter, Louis Carter and Monica Yang.
Identify the Minimum Vertex Cover of this network and present your answer in the following format: [UserA, UserB, UserC, UserD, ...].
user
{"directed": false, "multigraph": false, "graph": {}, "nodes": [{"name": "Paul Smith", "id": 2485560}, {"name": "Gavin Chavez", "id": 2485572}, {"name": "Andrew Dyer", "id": 4673317}, {"name": "Robert Smith", "id": 4673318}, {"name": "Emily Simmons", "id": 4673320}, {"name": "Michelle Brown", "id": 4673324}, {"name": "Chase Anthony", "id": 4673327}, {"name": "Jeremy Franklin", "id": 4673329}, {"name": "Jennifer Peck", "id": 4673333}, {"name": "Kathryn Sanchez", "id": 2485558}, {"name": "Matthew Johnson", "id": 2594869}, {"name": "Emily Wilkinson", "id": 4673336}, {"name": "Louis Carter", "id": 2485564}, {"name": "Nathaniel Bailey", "id": 4673340}, {"name": "Monica Yang", "id": 2404638}], "links": [{"source": 2485560, "target": 2404638}, {"source": 2485560, "target": 2485558}, {"source": 2485560, "target": 2485564}, {"source": 2485560, "target": 2485572}, {"source": 2485560, "target": 4673318}, {"source": 2485560, "target": 4673327}, {"source": 2485560, "target": 4673329}, {"source": 2485560, "target": 4673336}, {"source": 2485572, "target": 2404638}, {"source": 2485572, "target": 2485558}, {"source": 2485572, "target": 2485564}, {"source": 4673317, "target": 2485558}, {"source": 4673318, "target": 2485558}, {"source": 4673320, "target": 2485558}, {"source": 4673324, "target": 2485558}, {"source": 4673327, "target": 2485558}, {"source": 4673329, "target": 2485558}, {"source": 4673333, "target": 2485558}, {"source": 2485558, "target": 2404638}, {"source": 2485558, "target": 2485564}, {"source": 2485558, "target": 2594869}, {"source": 2485558, "target": 4673336}, {"source": 2485558, "target": 4673340}, {"source": 2485564, "target": 2404638}]}
Your task is to solve the Minimum Vertex Cover problem in the given social network. In this network, each node represents a user, and each edge represents a friendship connection. You need to identify the smallest subset of users such that every friendship connection has at least one user from this subset.

**Problem to Solve**

- Users in the network: Gavin Chavez, Andrew Dyer, Robert Smith, Nathaniel Bailey, Emily Simmons, Michelle Brown, Chase Anthony, Jeremy Franklin, Emily Wilkinson, Jennifer Peck, Kathryn Sanchez, Matthew Johnson, Paul Smith, Louis Carter, Monica Yang.
- Fiendship connections: Gavin Chavez and Monica Yang, Gavin Chavez and Kathryn Sanchez, Gavin Chavez and Paul Smith, Gavin Chavez and Louis Carter, Andrew Dyer and Kathryn Sanchez, Robert Smith and Kathryn Sanchez, Robert Smith and Paul Smith, Nathaniel Bailey and Kathryn Sanchez, Emily Simmons and Kathryn Sanchez, Michelle Brown and Kathryn Sanchez, Chase Anthony and Kathryn Sanchez, Chase Anthony and Paul Smith, Jeremy Franklin and Kathryn Sanchez, Jeremy Franklin and Paul Smith, Emily Wilkinson and Kathryn Sanchez, Emily Wilkinson and Paul Smith, Jennifer Peck and Kathryn Sanchez, Kathryn Sanchez and Monica Yang, Kathryn Sanchez and Paul Smith, Kathryn Sanchez and Louis Carter, Kathryn Sanchez and Matthew Johnson, Paul Smith and Monica Yang, Paul Smith and Louis Carter, Louis Carter and Monica Yang.
Identify the Minimum Vertex Cover of this network and present your answer in the following format: [UserA, UserB, UserC, UserD, ...].
test