
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 $$f(x)= \frac {\sin 2x - \cos 2x + 1}{2\sin x}$$.
(1) Find the domain of $f(x)$;
(2) Find the range of $f(x)$;
(3) Let $\alpha$ be an acute angle, and $\tan \frac {\alpha}{2} = \frac {1}{2}$, find the value of $f(\alpha)$.

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