
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) = cosx \* sinx + $\sqrt {3}cos^{2}x - \frac { \sqrt {3}}{2}$.
(1) Find the interval where the function f(x) is monotonically increasing.
(2) In acute triangle ABC, the sides opposite to angles A, B, and C are a, b, and c respectively. If f(A) = $\frac {1}{2}$, a = 3, b = 4, find the area of triangle ABC.

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