
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 \(\frac{\pi}{2}<\alpha<\pi\), find the range of real values of \( x \) that satisfy the equation \(\sin \alpha-\sqrt{3} \cos \alpha=\log _{2}\left(x^{2}-x+2\right)\).

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