
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 $f(x) = 4\sin^2\left(\frac{\pi}{4} + x\right) - 2\sqrt{3}\cos(2x) - 1$, and the condition $p$: $x < \frac{\pi}{4}$ or $x > \frac{\pi}{2}$, $x \in \mathbb{R}$. If condition $q$: $-3 < f(x) - m < 3$, and $\neg p$ is a sufficient condition for $q$, find the range of the real number $m$.

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