
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 $f(x)=4\sin^{2}(x+ \frac{π}{4})−2 \sqrt{3}\sin(2x+ \frac{π}{2})−1$, find the maximum and minimum values of $f(x)$ when $\frac{π}{4}⩽x⩽ \frac{π}{2}$. If the condition $q$ is "$|f(x)-m| < 2$" and $\neg p$ is a necessary condition for $\neg q$, find the range of $m$.

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