
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
Jana invented a 2022-digit number and whispered its digit sum to Petr. Petr calculated the digit sum of the number Jana told him and whispered the result to Zuzka. Zuzka also calculated the digit sum of the number she received from Petr and whispered the result, which was a two-digit number, to Adam. Adam did the same with the number from Zuzka and got a digit sum of 1.

What numbers could Petr have whispered to Zuzka? Determine all possibilities.

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