
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
Let $b_1, b_2, \ldots$ be a sequence defined by the following rules:
(i) $b_1 = 2$,
(ii) $b_{3n}=n\cdot b_n$ for any positive integer $n$.
What is the value of $b_{3^{100}}$?

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