
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 $f(x)=\frac{1}{3}x^{3}-ax^{2}+(a^{2}-1)x+b(a,b∈R)$.
(1) If $x=1$ is the extreme point of $f(x)$, find the value of $a$.
(2) If the equation of the tangent line to the graph of $y=f(x)$ at $(1,f(1))$ is $x+y-3=0$, find the maximum value of $f(x)$ in the interval $[-2,4]$.

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