
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]


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A fair cubic die with faces numbered 1, 2, 3, 4, 5, and 6 is rolled twice in succession. If the numbers facing up after the two rolls are $m$ and $n$ respectively, find the probability that the graph of the quadratic function $y=x^2+mx+n$ has exactly one intersection point with the x-axis.

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