
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 $f(x)=\cos ^{2}(x+ \frac {π}{12})+ \frac {1}{2}\sin 2x$.
(1) Find the interval where the function $f(x)$ is monotonically increasing;
(2) Find the coordinates of the first symmetry center of the function's graph on the right side of the $y$-axis.

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