
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 functions $f(x)=\cos ^{2}(x+ \frac {π}{12})$ and $g(x)=1+ \frac {1}{2}\sin 2x$.
(1) Let $x=x_{0}$ be an axis of symmetry of the graph of $y=f(x)$. Find the value of $g(x_{0})$.
(2) Find the interval(s) where the function $h(x)=f(x)+g(x)$ is strictly increasing.

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