
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, start at the same time from locations A and B, respectively, and travel back and forth between these two points. When A reaches point B for the fifth time, B simultaneously arrives at point B for the ninth time. Determine the total number of times A and B meet (including head-on encounters and overtaking) by the time A reaches point B for the 2015th time. Additionally, if they simultaneously arrive at point B, count it as a meeting.

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