
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 $f(x)=\frac{1}{3}{x^3}+3xf'(a)$ (where $a\in R)$, and $f(a)=\frac{7}{6}$, find:<br/>
$(1)$ The expression of $f(x)$;<br/>
$(2)$ The equation of the tangent line to the curve $y=f(x)$ at $x=a$.

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