
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 $f(x)=2\sin x\cdot\sin (x+ \frac {π}{3})$.
(I) Find the interval where the function $f(x)$ is monotonically increasing;
(II) In an acute triangle $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. The angle bisector of angle $A$ intersects $BC$ at $D$, and the line $x=A$ is a symmetry axis of the graph of function $f(x)$. $AD= \sqrt {2}BD=2$, find the side $a$.

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