
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
The route from point $B$ to $C$ begins with an uphill climb of $3 \text{ km}$, followed by a $5 \text{ km}$ horizontal section and ends with a downhill slope of $6 \text{ km}$ that has the same gradient as the initial uphill. A traveler started from $B$, turned back halfway, and returned to $B$ after $3$ hours and $36$ minutes. After resting, they took $3$ hours and $27$ minutes to reach $C$ and finally made the return trip in $3$ hours and $51$ minutes. What were the traveler's speeds on the horizontal path, uphill, and downhill?

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