
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
Given that $X=2 \cdot 3 \cdot 5 \cdot 7 \cdot 11$, and $\text{pow}(n)$ is the largest power of the largest prime that divides $n$, calculate the largest integer $m$ such that $X^m$ divides $\prod_{n=2}^{5400} \text{pow}(n)$.

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