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

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