
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 $f(x)=\sin \left(2x+ \frac{\pi}{6}\right)-2\cos^2{x}$.  
(I) Calculate the value of $f\left(\frac{\pi}{6}\right)$;  
(II) Find the maximum value of $f(x)$ in the interval $\left[-\frac{\pi}{3}, \frac{\pi}{6}\right]$.

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