
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
Patrick started walking at a constant rate along a straight road from school to the park. One hour after Patrick left, Tanya started running along the same road from school to the park. One hour after Tanya left, Jose started bicycling along the same road from school to the park. Tanya ran at a constant rate of  $2$  miles per hour faster than Patrick walked, Jose bicycled at a constant rate of  $7$  miles per hour faster than Tanya ran, and all three arrived at the park at the same time. The distance from the school to the park is  $\frac{m}{n}$  miles, where  $m$  and  $n$  are relatively prime positive integers. Find  $m + n$ .

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