
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
Let the function $f(x)$ have a derivative $f'(x)$ on $\mathbb{R}$, and for any real number $x$, it satisfies $f(x) = 4x^2 - f(-x)$. Given that when $x \in (-\infty, 0)$, $f'(x) < 4x$, determine the range of the real number $m$ such that $f(m + 1) \leq f(-m) + 4m + 2$.

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