
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 $f(x) = x^2 + 2ax$.

(1) Find the range of values for the real number $a$ if $f(x)$ is a monotonic function on $[-5, 5]$;

(2) If $y = f(x) - 2x$ is an even function, find the maximum and minimum values of $f(x)$;

(3) If $x \in [-5, 5]$, find the minimum value of $f(x)$.

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