
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
We say that a positive integer is guarani if the sum of the number with its reverse is a number that only has odd digits. For example,  $249$  and  $30$  are guarani, since  $249 + 942 = 1191$  and  $30 + 03 = 33$ .
a) How many  $2021$ -digit numbers are guarani?
b) How many  $2023$ -digit numbers are guarani?

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