
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
The sequence $\{a_n\}$ is an arithmetic sequence with first term $1$ and common difference $2$. Let $S_n$ denote the sum of its first $n$ terms. Compute the limit $\lim_{n\to\infty} \frac{S_n}{{a_n}^2}$.

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