
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 \( P(n) = \left(n-1^3\right)\left(n-2^3\right) \ldots\left(n-40^3\right) \) for positive integers \( n \). Suppose that \( d \) is the largest positive integer that divides \( P(n) \) for every integer \( n > 2023 \). If \( d \) is a product of \( m \) (not necessarily distinct) prime numbers, compute \( m \).

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