
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
Among all the factors of $11!$ (where $11! = 11 \times 10 \times \cdots \times 1$), the largest factor that can be expressed in the form $6k + 1$ (where $k$ is a natural number) is $\qquad$.

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