
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 $\overrightarrow{AC}=(\cos \frac {x}{2}+\sin \frac {x}{2},\sin \frac {x}{2})$ and $\overrightarrow{BC}=(\sin \frac {x}{2}-\cos \frac {x}{2},2\cos \frac {x}{2})$,
(1) Let $f(x)= \overrightarrow{AC} \cdot \overrightarrow{BC}$. Find the smallest positive period of $f(x)$ and its maximum and minimum values on the interval $[0, \frac {\pi}{2}]$.
(2) Let $x_{1}$ and $x_{2}$ be the two real roots of $f(x)= \frac { \sqrt {6}}{2}$ in the interval $(π,3π)$. Find the value of $x_{1}+x_{2}$.

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