
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 $f(x)=x^{2}+ax+2$.
(I) Find the value of the real number $a$ such that the function $y=f(x)$ is an even function in the interval $[-5,5]$;
(II) Find the range of values of the real number $a$ such that the function $y=f(x)$ is a monotonous function in the interval $[-5,5]$;
(III) Find the maximum value of $f(x)$ in the interval $[-5,5]$.

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