
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 $f(x)= \sqrt {3}sin( \frac {π}{2}-x)cos( \frac {3π}{2}+x)+sin^{2}x$.
(I) Find the smallest positive period and the monotonically increasing interval of the function $f(x)$;
(II) In triangle $ABC$, if the sides $a$, $b$, $c$ correspond to angles $A$, $B$, $C$ respectively, and $c= \sqrt {3}$, $f(C)= \frac {3}{2}$, and the area of triangle $ABC$ is $\frac { \sqrt {3}}{2}$, find the values of $a$ and $b$.

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