
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 finds himself at a point between his home and the stadium. He has two options to reach the stadium: walk directly to the stadium or walk back home and then ride his bicycle to the stadium. He rides 6 times as fast as he walks. If both routes take the same time, what is the ratio of Yan's distance from his home to his distance to the stadium?

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