
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 $f(x)=x^{3}+x$.
(1) Find the value of the definite integral $\int_{-3}^{3}(f(x)+x^{2})dx$;
(2) If a tangent line of the curve $y=f(x)$ passes through the point $(0,-2)$, find the equation of this tangent line.

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