
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
Two identical five-digit numbers were written on the wall. Pat added a one before one of these numbers, and Mat added a one after the other. Thus, they got two six-digit numbers, one of which was three times larger than the other.

What were the original five-digit numbers written on the wall?

(L. Hozová)

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