
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 $\{a_n\}$ with the first term $a_1=a$ and the sum of the first $n$ terms as $S_n$, and $-a_2$, $S_n$, $2a_{n+1}$ form an arithmetic sequence.  
(I) Determine whether the sequence $\{a_n\}$ is a geometric sequence and explain the reason;  
(II) If $a_5=32$, let $b_n=\log_2(a_1a_2\ldots a_n)$, find the value of $\frac{1}{b_1} + \frac{1}{b_2} + \ldots + \frac{1}{b_n}$.

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