
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 $f(x)=\frac{1}{3}x^{3}+2mx^{2}-\frac{1}{3}$ with derivative $f′(x)$, and $f′(-1)=9$.

(1) Find the equation of the tangent line to the function $y=f(x)$ at the point $(1,f(1))$;

(2) Find the monotonic intervals of the function $f(x)$.

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