
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 away from \(M\). They can walk at a speed of 6 km/h. In addition, 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 they meet a pedestrian \(C\) who is walking from \(N\) to \(M\). After the meeting, \(B\) continues on foot, and \(C\) rides the bicycle to meet \(A\), and then hands over the bicycle to \(A\), who then rides it to \(N\).

a) When should pedestrian \(C\) leave \(N\) so that \(A\) and \(B\) arrive at point \(N\) at the same time (if \(C\) walks at the same speed as \(A\) and \(B\))?

b) When should pedestrian \(C\) leave \(N\) so that the travel time for \(A\) and \(B\) to point \(N\) is minimized (considering \(C\) walks at the same speed as \(A\) and \(B\) and the travel time starts from when \(A\) and \(B\) leave \(M\) and ends when the last of them arrives at \(N\))?

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