
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 $$f(x)=\sin x\cos x+ \sqrt {3}\sin^{2}x- \frac { \sqrt {3}}{2}$$.
(1) Find the range of the function $f(x)$ when $x\in[0, \frac {π}{2}]$.
(2) In triangle $ABC$, $C$ is an acute angle, $f( \frac {C}{2})=- \frac {1}{2}$, $AB=3$, $A= \frac {π}{4}$, find the length of side $BC$.

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