
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
Alice starts to make a list, in increasing order, of the positive integers that have a first digit of 2. She writes $2, 20, 21, 22, \ldots$ but by the 1000th digit she (finally) realizes that the list would contain an infinite number of elements. Find the three-digit number formed by the last three digits she wrote (the 998th, 999th, and 1000th digits, in that order).

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