
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 12 km route consisting of a 6 km uphill track followed by a 6 km downhill return. Jack starts 10 minutes before Jill and runs at a speed of 14 km/hr uphill and 20 km/hr downhill. Jill runs at a speed of 16 km/hr uphill and 24 km/hr downhill. Calculate how far from the top of the hill they pass each other going in opposite directions (in km).
A) \( \frac{67}{21} \)
B) \( \frac{68}{21} \)
C) \( \frac{68}{22} \)
D) \( \frac{69}{21} \)

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