
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 $f(x)=\sin \left( \frac {\pi}{2}-x\right)\sin x- \sqrt {3}\cos ^{2}x.$  
(I) Find the smallest positive period and the maximum value of $f(x)$;  
(II) Discuss the monotonicity of $f(x)$ on the interval $\left[ \frac {\pi}{6}, \frac {2\pi}{3}\right].$

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