
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 curve $C$: $y=3x^{4}-2x^{3}-9x^{2}+4$.

$(1)$ Find the equation of the tangent line to curve $C$ at the point where the abscissa is $1$;

$(2)$ Does the tangent line obtained in question $(1)$ have other common points with curve $C$? If so, find them; if not, explain why.

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