
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 the sequence $\{ \sqrt {a_{n}}-n\}$, it is an arithmetic sequence with $a_{1}=9$ and $a_{2}=36$.
(1) Find the general term formula for the sequence $\{a_{n}\}$;
(2) Find the sum of the first $n$ terms, denoted as $S_{n}$, for the sequence $\{a_{n} - n^{2}\}$.

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