
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
We draw a circle that is tangent to the legs of a right angle $O A$ and $O B$; find a point $M$ on the circumference of the circle such that the perimeter of the rectangle $M P O Q$ is equal to a given length $2p$, where $M P \| O B$ and $M Q \| O A$.

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