
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 \(\{a_n\}\) where \(a_n=-4n+5\), and a geometric sequence \(\{b_n\}\) with a common ratio \(q\) satisfying \(q=a_n-a_{n-1} \ (n \geqslant 2)\), and \(b_1=a_2\), find the value of \(|b_1|+|b_2|+\ldots+|b_n|\).

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