
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 $f(x)=2\sin^{2}(\frac{\pi }{4}+x)+\sqrt{3}\cos 2x-1$.

(1) If there exists $x_{0} \in (0,\frac{\pi }{3})$ such that $f(x_{0})=1$, find the value of $x_{0}$.

(2) Let condition $p:x\in \left[\frac{\pi }{6},\frac{5\pi }{6} \right]$ and condition $q:-3 < f(x)-m < \sqrt{3}$, find the range of real number $m$ if $p$ is the sufficient condition for $q$.

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