
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A and B went to visit their high school math teacher, Mr. Zhang. During their visit, they played a game. Mr. Zhang's birthday is on the \\(m\\)th month and the \\(n\\)th day. Mr. Zhang told A the month \\(m\\) and told B the day \\(n\\), then Mr. Zhang listed the following \\(10\\) dates for them to choose from: February \\(5\\)th, February \\(7\\)th, February \\(9\\)th, May \\(5\\)th, May \\(8\\)th, August \\(4\\)th, August \\(7\\)th, September \\(4\\)th, September \\(6\\)th, September \\(9\\)th. After seeing the dates, A said, "I don't know, but you definitely don't know either." After hearing A's words, B said, "I didn't know before, but now I do." Then A said, "Oh, now I know too." What is Mr. Zhang's birthday?

Present the answer in LaTex format: \boxed{Your answer}
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