
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
Two people, $A$ and $B$, need to get from point $M$ to point $N$, which is 15 km away from $M$, as quickly as possible. They can walk at a speed of 6 km/h, and they have a bicycle that allows travel at 15 km/h. $A$ starts the journey on foot, while $B$ rides the bicycle until meeting with pedestrian $C$, who is walking from $N$ to $M$. After meeting, $B$ walks, and $C$ rides the bicycle to meet with $A$, then gives the bicycle to $A$, who then rides it to $N$. When should pedestrian $C$ leave $N$ so that the travel time for both $A$ and $B$ to reach $N$ is minimized? (Note: $C$ walks at the same speed as $A$ and $B$; the travel time is calculated from when $A$ and $B$ leave $M$ to when the last of them arrives at $N$.)

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