
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
Evaluate the expression \(\sqrt{\frac{2 \sin \alpha - \sin 2 \alpha}{2 \sin \alpha + \sin 2 \alpha}}\) for the following cases:
a) \(0 < \alpha < \pi\)
b) \(\pi < \alpha < 2\pi\)

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