
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 $$f(x)=2\sin x\cos x+ \sqrt {3}(2\cos^{2}x-1)$$.
(1) In triangle ABC, the lengths of the sides opposite to angles A, B, and C are a, b, and c respectively. The acute angle A satisfies $$f( \frac {A}{2}- \frac {π}{6})= \sqrt {3}$$. Find the measure of the acute angle A.
(2) Under the conditions of (1), if the circumradius of triangle ABC is 1, find the maximum area S of triangle ABC.

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