
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 sequence \( T_n \) defined as the sum of the first n positive integers, define
\( P_n = \frac{T_3^2}{T_3-1} \cdot \frac{T_4^2}{T_4-1} \cdot \frac{T_5^2}{T_5-1} \cdot \cdots \cdot \frac{T_n^2}{T_n-1} \) for \( n = 3, 4, 5, \cdots \). Find the value of \( P_{10} \).

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