
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 a function $f(x) = x^2 + ax + 5$ such that $f(-2+x) = f(-2-x)$ for all $x \in \mathbb{R}$. If the range of $f(x)$ is $[1, 5]$ when $x \in [m, 0]$ (where $m < 0$), find the range of values for the real number $m$.

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