
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
The magician Magimático calls three people from the audience: Ana, Beto, and Caio, to help in his mathematic magic. He tells each one to think of a number from 1 to 50, without revealing it to the magician, and share it with each of the other two participants. Then, each of them simultaneously replaces their number with the sum of the numbers of the other two. For example, Ana changes her number to the sum of Beto's and Caio's numbers. Magimático then asks them to repeat this process one more time. After completing the second exchange, he asks them to reveal their numbers. Ana says 104, Beto 123, and Caio 137. To everyone's surprise, Magimático correctly identifies the initial numbers chosen by the three. What were the initially chosen numbers?

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