
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 function $y=x^{2}-2x-11$, the equation of the tangent line at $x=2$ is $y=f(x)$. The sequence $\{a_{n}\}$ satisfies $a_{n}=f(n)$.
1. Find the general term formula and the sum of the first $n$ terms, $S_{n}$;
2. Find the minimum value of $nS_{n}$.

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