
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 Zoe start hiking from a trailhead toward a lookout point. Zoe is wearing a heavier backpack and walks slower. Chantal starts walking at $5$ miles per hour. After walking one-third of the distance to the lookout, the trail becomes very rocky, and Chantal reduces her speed to $3$ miles per hour. Upon reaching the lookout, she immediately turns around and descends the rocky part of the trail at $4$ miles per hour. She meets Zoe at the one-third point on the way back. What is Zoe's average speed, in miles per hour, until they meet?

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