
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
Pedrinho wrote all the integers between 100 and 999 where the sum of the digits is 12. For example, the numbers 129 and 750 are among the written numbers.

a) How many written numbers have only two identical digits?

b) How many written numbers consist only of odd digits?

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