
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
Chantal and Jean start hiking from the trailhead toward a lookout point. Chantal is faster but will face varying terrain conditions. Chantal walks the first third of the trail at a speed of 3 miles per hour. The next third, which is steep, she walks at 1.5 miles per hour. The last third, which is smooth, she walks at 4 miles per hour. After reaching the lookout, Chantal immediately turns around and walks back. During her return, she walks the smooth and steep parts at 3 miles per hour and 2 miles per hour respectively. She meets Jean, who walks at a constant speed throughout. If they meet exactly four hours after they started, what was Jean's average speed, in miles per hour?
A) \( \frac{3}{5} \)
B) \( \frac{9}{13} \)
C) 0.75
D) \( \frac{144}{200} \)
E) \( \frac{15}{20} \)

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