
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 $B$, must get from point $M$ to point $N$, which is 15 km from $M$, as quickly as possible. They can walk at a speed of 6 km/h. Additionally, they have a bicycle that can be ridden at a speed of 15 km/h. $A$ starts the journey on foot, while $B$ rides the bicycle until meeting a pedestrian $C$ coming from $N$ and $M$. Then, $B$ continues on foot, and $C$ rides the bicycle until meeting $A$ and hands over the bicycle, with which $A$ rides to $N$. When should pedestrian $C$ leave from $N$ so that the time taken by both $A$ and $B$ to reach $N$ is minimized? (Note: $C$ walks at the same speed as $A$ and $B$; the time taken is measured from the moment $A$ and $B$ leave $M$ until the last person arrives in $N$.)

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