
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 that
\[
\cos^2 \alpha \sin^2 \beta + \sin^2 \alpha \cos^2 \beta = \cos \alpha \sin \alpha \cos \beta \sin \beta,
\]
find the value of
\[
\frac{\sin^2 \beta \cos^2 \alpha}{\sin^2 \alpha} + \frac{\cos^2 \beta \sin^2 \alpha}{\cos^2 \alpha}.
\]

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