
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 somewhere between his home and the school. He can either walk directly to school or walk back home and then ride his bicycle to school. He rides 5 times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's distance from his home to his distance from the school?

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