
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
\[ 4.51 \cot^2 \alpha + \cot^2 \beta - \frac{2 \cos (\beta - \alpha)}{\sin \alpha \sin \beta} + 2 = \frac{\sin^2 (\alpha - \beta)}{\sin^2 \alpha \sin^2 \beta} \]

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