
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 geometric sequence $\{a\_n\}$ satisfies $a\_2=2a\_1$, and $a\_2+1$ is the arithmetic mean of $a\_1$ and $a\_3$.
(1) Find the general term formula of the sequence $\{a\_n\}$;
(2) If $b\_n=a\_n-2\log \_{2}a\_n$, find the sum of the first $n$ terms $S\_n$ of the sequence $\{b\_n\}$.

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