
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
Joãozinho collects natural numbers whose unit digit is the sum of the other digits. For example, he collected 10023, because $1+0+0+2=3$.

a) In Joãozinho's collection, there is a number with 4 digits whose unit digit is 1. What is that number?

b) What is the largest number without the digit 0 that can appear in the collection?

c) What is the largest number without repeated digits that can appear in the collection?

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