
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
Given Chantal and Jean start hiking from a trailhead toward a lookout point, and Jean moves slower due to a heavier pack. If Chantal begins her hike at $5$ miles per hour, after walking for one-fourth of the total distance, she reduces her speed to $2.5$ miles per hour when the path becomes rocky. She then descends the rocky path at $4$ miles per hour and meets Jean at the one-fourth point on her return, determine Jean's average speed, in miles per hour, until they meet.

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