
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
A hiking trail leaves from point \(P\). The trail consists of a flat section from point \(P\) to point \(Q\), followed by an uphill section from \(Q\) to a viewing platform at point \(R\). A hiker walked from \(P\) to \(Q\) to \(R\) and back from \(R\) to \(Q\) to \(P\). The hiker's speed was \(4 \text{ km/h}\) on the flat section in both directions, \(3 \text{ km/h}\) while walking uphill, and \(6 \text{ km/h}\) while walking downhill. If the hiker left \(P\) at 1:00 p.m., spent exactly 1 hour at \(R\), and returned to \(P\) at 8:00 p.m. on the same day, what was the total distance walked by the hiker?

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