
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 that the sequence $\{a_n\}$ is a geometric sequence with the first term being $32$, and $S_n$ is the sum of the first $n$ terms, and it is given that $\frac{S_6}{S_3} = \frac{9}{8}$, then the sum of the first $10$ terms of the sequence $\{|\log_2 a_n|\}$ is ______.

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