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

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