
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, start from points A and B respectively at the same time and keep traveling back and forth between A and B. When A reaches point B for the 5th time, B happens to return to point B for the 9th time. How many times have they encountered each other (including head-on and overtaking encounters, and also if they arrive at point B simultaneously, it counts as an encounter) by the time A reaches point B for the 2015th time?

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