
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
One day in the 20th century (1900-1999), a younger brother said to his older brother: "Brother, look, if you add up the four digits of the year you were born, it gives my age." The elder brother responded: "Dear brother, you are right! The same applies to me, if I add up the four digits of the year you were born, it gives my age. Additionally, if we swap the two digits of our respective ages, we can get each other's age." Given that the two brothers were born in different years, in which year did this conversation take place?

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