
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
Oliver is between his apartment and the library. He has the option to walk directly to the library or walk back to his apartment and then cycle to the library. He rides 5 times as fast as he walks. If both options take the same amount of time, find the ratio of the distance between his apartment to the library and the distance from his current location to the library.

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