
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 a trailhead toward a fire tower that is 6 miles away. Chantal, walking faster, starts at a pace of 5 miles per hour for the first 3 miles. The next 3 miles of the trail becomes steep, and she reduces her speed to 3 miles per hour. Once reaching the tower, she turns around and comes back down the steep trail at a speed of 4 miles per hour. She meets Jean one-third of the way up the steep ascent on her way down. Calculate the time it takes Chantal to reach this meeting point and then calculate Jean's average speed in miles per hour until they meet.

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