
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 geometric sequence \{a_n\} that satisfies $a_2 = 2a_1$, and $a_2 + 1$ is the arithmetic mean between $a_1$ and $a_3$.
(1) Find the general formula for the $n^{th}$ term of the sequence \{a_n\}.
(2) If $b_n = a_n - 2\log_2a_n$, find the sum of the first $n$ terms of the sequence \{b_n\}, denoted as $S_n$.

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