
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 pedestrian left point $A$ for a walk at a speed of $v$ km/h. After he had walked 6 km away from $A$, a cyclist left $A$ following him at a speed that was 9 km/h faster than the pedestrian's speed. When the cyclist caught up with the pedestrian, they turned back and returned together to $A$ at a speed of 4 km/h. At what value of $v$ will the pedestrian's total walking time be minimized?

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