
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
Let Chantal and Jean start hiking from a trailhead toward a fire tower. Chantal starts off at a speed of $5$ miles per hour. At the halfway point, when the trail becomes steeper, she reduces her speed to $2.5$ miles per hour. Upon reaching the halfway point in the first segment, Chantal takes a break and then turns around. She then descends at $4$ miles per hour to meet Jean at the halfway point. Given the total time it takes for this process to complete, determine Jean's average speed in miles per hour.

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