
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 segment $A B=2 d$ is bisected perpendicularly by the line $e$. On this line $e$, the segment $R S=d$ slides. The lines $A R$ and $B S$ intersect at point $P$. What is the locus of point $P$?

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