
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 $\{a_n\}$ with the first term $a_1=2$, and $a_{n+1}=3a_n+2$ for $n\in \mathbb{N}^*$; let $b_n=\log_{3}(a_n+1)$, then the sum $b_1+b_2+b_3+\ldots+b_{100}=$ ______.

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