
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
John and Jane run an initial 8 km uphill and return 6 km downhill to the starting point from a common starting point. John receives a 12 minute head start and runs at a rate of 10 km/hr uphill and 15 km/hr downhill, while Jane runs at 12 km/hr uphill and 18 km/hr downhill. Determine the distance from the top of the hill where they will pass each other going in opposite directions.

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