
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
Let  $n!=n\cdot (n-1)\cdot (n-2)\cdot \ldots \cdot 2\cdot 1$ .For example,  $5! = 5\cdot 4\cdot 3 \cdot 2\cdot 1 = 120.$  Compute  $\frac{(6!)^2}{5!\cdot 7!}$ .


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