
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 $f(x) = \sin x \cos x - \sqrt {3} \cos (π+x) \cos x$ where $x \in R$
(1) Find the smallest positive period of $f(x)$;
(2) If $\sin (π+α)= \frac {4}{5}$ and $|α| < \frac {π}{2}$, find the value of $f(x) - \frac {\sqrt {3}}{2}$.

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