
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 $\overrightarrow{OM}$ and $\overrightarrow{ON}$ be two unit vectors with an angle of $60^\circ$ between them, and let $\overrightarrow{OP} = x \cdot \overrightarrow{OM} + y \cdot \overrightarrow{ON}$, where $x$ and $y$ are real numbers. If triangle $\triangle PMN$ is a right triangle with $M$ as the right angle vertex, then the value of $x - y$ is _____.

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