
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
Yan is situated between his home and the stadium. To get to the stadium, Yan can either walk directly there or return home first and then ride his bicycle to the stadium. He now rides 10 times as fast as he walks, and both routes take the same amount of time. Determine the ratio of the distance from Yan's current position to his home and to the stadium.

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