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

(1) Find the smallest positive period of $f(x)$;

(2) Find the maximum and minimum values of $f(x)$ on the closed interval $\[-{{\pi }\over{3}},{{\pi }\over{6}}\]$.

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