
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 a sequence $\left\{ a_n \right\}$ with the general term formula $a_n=\dfrac{1}{(n+1)^2}$ $(n\in N_+)$, let $f(n)=(1-a_1)(1-a_2)\cdot\cdot\cdot(1-a_n)$. Try to deduce the expression for $f(n)$ by calculating the values of $f(1), f(2), f(3)$.

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