
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
In the book "Nine Chapters on the Mathematical Art," there is a problem stated as follows:  
"Two people, A and B, each hold an unknown amount of money. If A receives half of B's money, A will have 50 units of money. If A gives two-thirds of his money to B, B will also have 50 units of money. How much money does A and B each have?"  
Please solve the above problem.

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