
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 $f(x)= \frac{1}{3}x^{3}+x^{2}-3x+a$,
(I) Find the interval where $f(x)$ is monotonically decreasing;
(II) If the minimum value of $f(x)$ in the interval $[-2,2]$ is $2$, find its maximum value in this interval.

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