
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 swimmer goes downstream in a river from point \( P \) to point \( Q \), and then crosses a still lake to point \( R \), taking a total of 3 hours. When the swimmer travels from \( R \) to \( Q \) and then back to \( P \), it takes 6 hours. If the lake water is also flowing with the same speed as the river, the journey from \( P \) to \( Q \) and then to \( R \) takes \(\frac{5}{2}\) hours. Under these conditions, how many hours does it take for the swimmer to travel from \( R \) to \( Q \) and then to \( P \)?

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