
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 $f(x)=2\sin (x- \frac {π}{3})\cos x+\sin x\cos x+ \sqrt {3}\sin ^{2}x (x\in R)$.
(1) Find the interval(s) where $f(x)$ is monotonically increasing.
(2) In $\triangle ABC$, $B$ is an acute angle, $f(B)= \sqrt {3}$, $AC=4 \sqrt {3}$, and $D$ is a point on $BC$ such that $AB=AD$. Find the maximum value of the perimeter of $\triangle ADC$.

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