
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
The circles \( k_{1} \) and \( k_{2} \) (having different radii) touch each other at point \( T \). A line \( e \) passing through point \( T \) intersects the circles at points \( M_{1} \) and \( M_{2} \), respectively. The lines \( O_{1} M_{2} \) and \( O_{2} M_{1} \) intersect at point \( P \). What path does \( P \) trace out as the line \( e \) revolves around \( T \)?

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