
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 swimmers start from points that are $12$ miles apart. If they swim towards each other, they meet in $3$ hours. However, if they swim in the same direction, the faster swimmer catches up with the slower one in $6$ hours. Calculate the ratio of the speed of the faster swimmer to the slower swimmer.

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