
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 $\{a_n\}$ with the general formula $a_n= \frac {1}{(n+1)^{2}}$ ($n\in\mathbb{N}^{*}$), and let $b_n=(1-a_1)(1-a_2)\ldots(1-a_n)$, try to deduce the general formula of $\{b_n\}$ by calculating the values of $b_1$, $b_2$, and $b_3$.

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