
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
Jack and Jill run a total distance of 12 km. They start at the same point, run 6 km up a hill, and return to the starting point by the same route. Jack has a 10-minute head start and runs at a rate of 15 km/hr uphill and 20 km/hr downhill. Jill runs at 18 km/hr uphill and 24 km/hr downhill. Find the distance from the top of the hill at which they meet each other going in opposite directions.

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