
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
A and B are two towns 100 kilometers apart. Person A and Person B start walking towards each other from towns A and B, respectively. The speed of person A is four times the speed of person B. They meet after 3 hours. Then, A continues to move forward, turning back immediately upon reaching town B and continues this cycle of motion until B reaches town A, at which point both stop moving.
(1) Determine the speeds of person A and B.
(2) During the entire motion process, how many times do A and B meet in total, and calculate the time of each encounter.

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