
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 $f(x)=2 \sqrt {3}\cos ( \frac {π}{2}-x)\cos x-\sin ^{2}x+\cos ^{2}x (x\in R)$.
(1) Find the smallest positive period and the monotonically increasing interval of the function $f(x)$;
(2) If $f(x_{0})= \frac {6}{5}$, $x_{0}\in[ \frac {π}{4}, \frac {π}{2}]$, find the value of $\cos 2x_{0}$.

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