
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
Three cyclists are initially $8$ miles apart and start at the same time. If they all travel in the same direction, the fastest and the slowest would take $4$ hours to meet. If they travel towards each other, the fastest would meet the slowest in $1$ hour. Find the ratio of the speed of the fastest cyclist to the speed of the slowest cyclist.

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