
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
The full marks for this question are 12. It is known that the function $f(x) = x^2 + 2ax + 2$, for $x \in [-5,5]$.  
(1) When $a = -1$, find the maximum and minimum values of the function.  
(2) Determine the range of real numbers $a$ such that $y = f(x)$ is a monotonic function on the interval $[-5,5]$.

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