
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
For each pair of numbers \( x \) and \( y \), let \( s(x, y) \) denote the smallest of the numbers \( x \), \( 1 - y \), and \( y - x \). What is the largest possible value that \( s(x, y) \) can take?

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