
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 \( a \star b = \sin a \cos b \) for all real numbers \( a \) and \( b \). If \( x \) and \( y \) are real numbers such that \( x \star y - y \star x = 1 \), what is the maximum value of \( x \star y + y \star x \)?

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