
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 base  $4$  repeating decimal  $0.\overline{12}_4$  can be expressed in the form  $\frac{a}{b}$  in base 10, where  $a$  and  $b$  are relatively prime positive integers. Compute the sum of  $a$  and  $b$ .

*2020 CCA Math Bonanza Team Round #2*

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