
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
A positive integer is *brazilian* if the first digit and the last digit are equal. For instance,  $4$  and  $4104$  are brazilians, but  $10$  is not brazilian. A brazilian number is *superbrazilian* if it can be written as sum of two brazilian numbers. For instance,  $101=99+2$  and  $22=11+11$  are superbrazilians, but  $561=484+77$  is not superbrazilian, because  $561$  is not brazilian. How many  $4$ -digit numbers are superbrazilians?

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