
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 $f(x)=ax^{2}+bx+3$ ($a\neq 0$), its derivative is $f′(x)=2x-8$.

$(1)$ Find the values of $a$ and $b$;

$(2)$ Let the function $g(x)=e^{x}\sin x+f(x)$, find the equation of the tangent line to the curve $g(x)$ at $x=0$.

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