
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
The numbers $2005$, $2231$, and $2126$ have something in common: each is a $4$-digit number beginning with $2$ that has exactly two identical digits. How many such numbers are there?

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