
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 $f\left(x\right)=2{\sin }^{2}x\left( \frac{π}{4}+x\right)- \sqrt{3}\cos 2x-1, x∈R$.

(1) If the graph of the function $h(x)=f(x+t)$ is symmetric about the point $\left( -\frac{\pi }{6},0 \right)$, and $t∈(0,π)$, find the value(s) of $t$.

(2) Let $p: x ∈ \left[\frac{\pi }{4},\frac{\pi }{2} \right]$ and $q: \left| f(x)-m \right|≤ 3$. If $p$ is a sufficient condition for $q$, find the range of values for the real number $m$.

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