
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 $f(x)=\sin (2x+ \frac {π}{6})+ \sin (2x- \frac {π}{6})+ \cos 2x+1$,
(1) Find the symmetry center and the monotonically increasing interval of the function $f(x)$;
(2) In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$, respectively. If $f(A)=3, B= \frac {π}{4}, a= \sqrt {3}$, find $AB$.

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