
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 an arithmetic sequence $\{a_n\}$ where $a_1 = 2$ and $a_2^2 = a_1a_5$,
(1) Find the general formula for the sequence $\{a_n\}$.
(2) Let $S_n$ denote the sum of the first n terms of the sequence $\{a_{2n-1}\}$. Find $S_n$.

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