
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 25 distinct prime numbers \( p_1, p_2, \cdots, p_{25} \) each less than or equal to 2004, find the largest integer \( T \) such that any positive integer less than or equal to \( T \) can be expressed as the sum of distinct positive divisors of \( \left(p_{1} p_{2} \cdots p_{25}\right)^{2004} \).

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