
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 each run a total of 12 km, starting from the same point and running 6 km up a hill, then returning to the starting point by the same route. Jack starts 15 minutes (or $\frac{1}{4}$ hours) ahead of Jill. Jack runs at a rate of 12 km/hr uphill and 18 km/hr downhill. Jill runs at a rate of 14 km/hr uphill and 20 km/hr downhill. How far from the top of the hill are they when they first meet each other?
A) $\frac{85}{32}$
B) $\frac{87}{32}$
C) $\frac{89}{32}$
D) $\frac{90}{32}$

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