
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
Chose rational numbers \(a\) and \(b\) from the interval \([0,1)\), where both can be expressed as fractions of the form \(\frac{n}{d}\) with \(n\) and \(d\) integers, and \(d\) can take any value from 1 to 6. What is the probability that \[(\text{cos}(a\pi)+i\text{sin}(b\pi))^4\] results in a real number?

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