
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
Person A and Person B start from points $A$ and $B$ respectively and walk towards each other. The first time they meet, it is 100 meters away from point $B$. After meeting, Person A doubles their speed. Person A reaches point $B$, turns around immediately, and catches up with Person B when Person B is 50 meters away from point $A$. How long is the distance between points $A$ and $B$?

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