
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 $f(x)=\frac{1}{3}{x}^{3}+{x}^{2}+ax(a∈R)$, the tangent line of the curve $y=f\left(x\right)$ at the point $\left(1,f\left(1\right)\right)$ is parallel to the line $y=0$.  
$(1)$ Find the value of $a$;  
$(2)$ Find the extreme values of the function $f\left(x\right)$.

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