
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 joggers start from points that are 12 miles apart and begin jogging towards each other at the same time. If they meet in 2 hours when moving towards each other, but take 6 hours to cover the same distance when one chases the other while moving in the same direction, find the ratio of the speed of the faster jogger to that of the slower jogger.

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