
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 $P$, $M$, $N$ are three distinct points on the circle $O:x^{2}+y^{2}=1$, and $\overrightarrow{OM} \cdot \overrightarrow{ON} = 0$, if there exist real numbers $m$, $n$, such that $\overrightarrow{OP} = m\overrightarrow{OM} + n\overrightarrow{ON}$, then the relationship between the real numbers $m$, $n$ is \_\_\_\_.

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