
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 $f(x)=\cos ^{2}x$ and $g(x)= \frac {1}{2}+ \sqrt {3}\sin x\cos x$.
(1) If the line $x=a$ is an axis of symmetry of the graph of the function $y=f(x)$, find the value of $g(2a)$;
(2) If $0\leqslant x\leqslant \frac {\pi}{2}$, find the range of values of $h(x)=f(x)+g(x)$.

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