
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 $f(x) = x^{2} + 2ax + 2$ where $x \in [-5,5]$ (and $a$ is a constant),
(1) When $a = -1$, find the maximum and minimum values of $f(x)$,
(2) If $f(x)$ is a monotonic function on its domain, determine the range of values for $a$.

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