
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, 8 miles apart, begin at the same point but head in different directions. They would meet each other in 2 hours if they jogged towards each other, but they would take 4 hours to be 8 miles apart again if they jogged away from each other in the same direction at the beginning. What is the ratio of the speed of the faster jogger to the slower jogger?

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