
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
A fair six-sided die with faces numbered 1, 2, 3, 4, 5, 6 is rolled twice. Let $m$ and $n$ denote the outcomes of the first and second roll, respectively. List all basic events and find:
1. The probability that the quadratic equation $x^2 + mx + n^2 = 0$ has two distinct real roots.
2. The probability that $\frac{m}{n}$ is not an integer.

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