
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 $f(x)=4\sin x\cos (x+ \frac {π}{3})+ \sqrt {3}$, $x\in[0, \frac {π}{6}]$.
(1) Find the range of the function $f(x)$;
(2) The two sides of an acute triangle $\triangle ABC$ have lengths $a$ and $b$, which are the minimum and maximum values of the function $f(x)$, respectively. The radius of the circumcircle of $\triangle ABC$ is $\frac {3 \sqrt {2}}{4}$. Find the area of $\triangle ABC$.

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