Agent Implementation of MathChat

[yiranwu0]

Implement the MathChat paper with the current agent framework:

• Put the specified math problem-solving prompt in system message of AssistantAgent for the LLM. If the behavior is not desired, the assistant agent need to be modified to accept this prompt in user message.
• Implement a MathUserProxyAgent from UserProxyAgent, need to inherit the autoreply function.
• MathChat proposes a conversational framework to solve math problems, which is equivalent to interactions between the two agents. Building on the agents also allow human inputs.

### Tasks
- [x] Review PR https://github.com/microsoft/FLAML/pull/1056
- [x] Evaluate the performance of AssistantAgent and UserProxyAgent on math problem solving (on several representative problems)
- [ ] Agent implementation of MathChat. PR made and approvals from reviewers pending in https://github.com/microsoft/FLAML/pull/1076
- [ ] Update arxiv: Update link to implementation(keep the old one for the purpose of reproducing the exp results)
- [ ] Update FLAML's autogen documentation: mention MathChat
- [ ] Write a blogpost about MathChat

[sonichi]

What does "Put the specified math problem-solving prompt in system message of AssistantAgent for the LLM." mean? A complete replacement or a modification? There are certain designs in the existing prompt of AssistantAgent that makes it collaborate w/ the UserProxyAgent. Would you like to keep those working designs?

[yiranwu0]

I mean that when calling the AssistantAgent, I will not use the default system_message but input one. I will implement a corresponding MathUserProxyAgent, and I will modify the autoreply function. It will follow the working design, however the autoreply will be very different from the base proxyagent.

[qingyun-wu]

@kevin666aa, I revised the task list.