
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 travel from point $M$ to point $N$, which is 15 km from $M$. They can walk at a speed of 6 km/h. Additionally, they have a bicycle which allows them to travel at a speed of 15 km/h. $A$ and $B$ leave $M$ at the same time: $A$ walks while $B$ rides the bicycle until meeting a pedestrian $C$ who is walking from $N$ to $M$. Then $B$ continues walking, and $C$ rides the bicycle until meeting $A$, hands over the bicycle to $A$, who then rides it to $N$. When should $C$ leave $N$ to ensure that $A$ and $B$ arrive at $N$ simultaneously if $C$ walks at the same speed as $A$ and $B$?

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