
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 circuit. First, they run 7 km to a certain point and then the remaining 5 km back to the starting point by different, uneven routes. Jack has a 12-minute head start and runs at the rate of 12 km/hr uphill and 15 km/hr downhill. Jill runs 14 km/hr uphill and 18 km/hr downhill. How far from the turning point are they when they pass each other, assuming their downhill paths are the same but differ in uphill routes (in km)?
A) $\frac{226}{145}$  
B) $\frac{371}{145}$  
C) $\frac{772}{145}$  
D) $\frac{249}{145}$  
E) $\frac{524}{145}$

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