
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
Define a set \( \mathcal{T} \) of distinct positive integers such that for every integer \( y \) in \( \mathcal{T}, \) the geometric mean of the values obtained by omitting \( y \) from \( \mathcal{T} \) remains a positive integer. In addition, assume that 1 is a member of \( \mathcal{T} \) and the largest element is 2500. What is the maximum size that \( \mathcal{T} \) can contain?

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