
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 $\{a_n\}$ where $a_n = -3n + 4$, and the geometric sequence $\{b_n\}$ with common ratio $q$ satisfying $q = a_n - a_{n-1} (n \geqslant 2)$ and $b_1 = a_1$, find the maximum value of $n$ such that $\frac{1}{|b_1|} + \frac{1}{|b_2|} + \ldots + \frac{1}{|b_n|} < \frac{121}{81}$.

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