
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
Let \( x, y \in \mathbf{R} \), and \(\frac{\sin ^{2} x-\cos ^{2} x+\cos ^{2} x \cos ^{2} y-\sin ^{2} x \sin ^{2} y}{\sin (x+y)} = 1 \). Then \( x - y = \) ___

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