
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 $f(x)=6x^{2}-f(-x)$. When $x\in(-\infty,0)$, $2f'(x)+1 < 12x$. If $f(m+2)\leqslant f(-2m)+12m+12-9m^{2}$, determine the range of the real number $m$.

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