
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
Given a student multiplied 66 by the repeating decimal \(1.\overline{ab}\) (where \(a\) and \(b\) are two digits), but the student did not notice the repeating nature and incorrectly multiplied 66 by \(1.ab\), and the difference between the correct and incorrect answers is 0.5, find the two-digit number \(\overline{ab}\).

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