
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
Two cyclists are $2k$ miles apart. When traveling in the same direction, they meet in $3r$ hours, and when traveling in opposite directions, they pass each other in $2t$ hours. Given that the speed of the faster cyclist is twice the speed of the slower cyclist when they travel towards each other, find the ratio of the speed of the faster cyclist to that of the slower cyclist when they travel in the same direction.

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