
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
An athlete decided to run a $15 \mathrm{~km}$ race. They started by running $5 \mathrm{~km}$ south, then turned east and ran another $5 \mathrm{~km}$, and finally turned north, running the remaining $5 \mathrm{~km}$. After this route, the athlete discovered, to their amazement, that they were at the starting point.

Find two possible points on the Earth where this athlete could have started their run.

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