
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
Let the function $f(x)=2x^{3}-3(a+1)x^{2}+6ax+8$, where $a\in \mathbb{R}$. It is known that $f(x)$ has an extremum at $x=3$.

$(1)$ Find the explicit formula of $f(x)$;

$(2)$ Find the equation of the tangent line to $f(x)$ at the point $A(1,16)$.

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