
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 the integer \( n \geq 2 \), let \( \text{pow}(n) \) be the largest power of the largest prime that divides \( n \). Compute the smallest integer \( m \) such that \( 2310^m \) divides \( \left(\sum_{n=2}^{4000} \text{pow}(n)\right)^2. \)

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