
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 and David are practicing adding decimal numbers by each writing down a number and then adding these two numbers together. The result of their last exercise was 11.11. David's number had the same number of digits before and after the decimal point, and so did Jana's number. David's number was written using mutually different digits, while Jana's number had exactly two identical digits. Determine the largest possible number David could have written.

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