
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 $f(x)=x^{3}+ax^{2}+bx+1$, its derivative $f'(x)$ satisfies $f'(1)=2a$ and $f'(2)=-b$, where $a$ and $b$ are constants.

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

(2) Let $g(x)=f(x)e^{-x}$. Find the extreme values of the function $g(x)$.

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