
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 general term formula of the sequence $a\_n$, where $a\_n = \frac{1}{(n+1)^2} (n \in \mathbb{N_+})$, let $f(n) = (1 - a\_1)(1 - a\_2) \dots (1 - a\_n)$. By calculating the values of $f(1)$, $f(2)$, and $f(3)$, try to infer the value of $f(n)$.

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