
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 $\{a_n\}$ that satisfies: $a_1=1$, $a_2=2$, $a_3=3$, $a_4=4$, $a_5=5$, and for $n\geq5$, $a_{n+1}=a_1a_2\ldots a_n-1$. If the sequence $\{b_n\}$ satisfies for any $n\in\mathbb{N}^*$, $b_n=a_1a_2\ldots a_n-a_1^2-a_2^2-\ldots-a_n^2$, then find $b_5$; and for $n\geq5$, find $b_n$.

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