
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 $AB$ of unit length moves in the Cartesian coordinate system in such a way that point $A$ is always on the $x$-axis and point $B$ is always on the $y$-axis. Write down the equation of the curve traced out by the feet of the perpendiculars dropped from the origin to segment $AB$.

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