
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
In the famous book "Algorithm for Direct Calculation" by the Chinese mathematician Cheng Dawei of the Ming Dynasty, there is a well-known math problem:

"One hundred mantou for one hundred monks, three big monks have no dispute, three small monks share one, how many big and small monks are there?"

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