
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
On the surface of the Earth, consider all possible points whose geographic latitude is equal to their longitude. Find the geometric locus of the projections of these points on the plane of the equator.

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