
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 arithmetic sequence $\{a_n\}$ where $a_n=-4n+5$, and the geometric sequence $\{b_n\}$ with a common ratio $q$ satisfying $q=a_n-a_{n-1}$ (for $n \geq 2$), and given that $b_1=2$, find the sum of the absolute values $|b_1|+|b_2|+\ldots+|b_n|$.

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