
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 individuals $A$ and $B$ need to travel from point $M$ to point $N$, which is located 15 km from $M$. They can walk at a speed of 6 km/h. Additionally, they have a bicycle available that can be ridden at a speed of 15 km/h. Person $A$ starts walking, while $B$ rides the bicycle until encountering a pedestrian $C$ walking from $N$ to $M$. After meeting $C$, $B$ continues on foot, and $C$ takes the bicycle until meeting $A$, after which $A$ takes the bicycle to reach $N$. At what time should pedestrian $C$ leave from $N$ so that $A$ and $B$ arrive at point $N$ simultaneously (assuming $C$ walks at the same speed as $A$ and $B$)?

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