
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
Among the natural numbers greater than 1999, calculate the maximum number of numbers that can be selected so that the sum of the last two digits of any two of them adds up to 0.

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