
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 $f(x)=\sin \left(2x+\frac{\pi }{3}\right)+\sin \left(2x-\frac{\pi }{3}\right)+2\cos ^{2}(x)-1$, where $x\in R$.

(1) Simplify the function $f(x)$ in the form of $A\sin (\omega x+\phi )$ $(A,\omega > 0,0 < \phi < \frac{\pi }{2})$

(2) Find the maximum and minimum values of the function $f(x)$ in the interval $\left[-\frac{\pi }{4},\frac{\pi }{4}\right]$.

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