
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 $f(x)=2\sin x\cos x-\sqrt{3}\cos 2x+1$ $(x\in \mathbb{R})$.

$(1)$ Simplify $f(x)$ and find the smallest positive period of $f(x)$;

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

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