
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 $\overrightarrow {m}$=($\frac {1}{2}$sinωx, $\frac { \sqrt {3}}{2}$) and $\overrightarrow {n}$=(cosωx, cos$^2$ωx- $\frac {1}{2}$), where x∈R, ω>0, and the function f(x) = $\overrightarrow {m}$⋅$\overrightarrow {n}$. The minimum distance from one of the symmetry centers of the graph of y=f(x) to its axis of symmetry is $\frac {π}{2}$.
(1) Find the interval(s) where f(x) is monotonically increasing and the symmetry center.
(2) In triangle ABC, the sides opposite angles A, B, and C are a, b, and c, respectively. If f(A) = $\frac {1}{2}$, sinB = $\frac {4}{5}$, and a = $\sqrt {3}$, find the area of triangle ABC.

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