
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 ${a_n}$ is an arithmetic sequence with all terms non-zero, $S_n$ represents the sum of its first $n$ terms, and for any positive integer $n$, $a_n^2 = S_{2n-1}$, find $a_n$.

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