
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 mathematician left point A for point B. After some time, a physicist left point A as well. The physicist caught up with the mathematician after 20 km, and without stopping, continued to point B and then turned back. They met for the second time 20 km away from point B. Each then continued in their respective directions. Upon reaching points A and B respectively, they turned back and headed towards each other again. At how many kilometers from point A will they meet for the third time, if the distance between points A and B is 100 km?

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