
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, and $a_1 + a_2 = 9, a_2 + a_3 = 18$,

  (1) Find the general formula for the sequence $\{a_n\}$;

  (2) Given that the sequence $\{b_n\}$ satisfies $b_n = a_n + 2n$, find the sum of the first $n$ terms of $\{b_n\}$, $S_n$.

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