
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
(1) A standard six-sided die, with faces numbered 1 to 6, is rolled twice. Let $(m, n)$ be the coordinates of point $P$ corresponding to the numbers rolled. Find the probability that point $P$ falls within the region defined by $\begin{cases} x + y \leqslant 6 \\ x \geqslant 0 \\ y \geqslant 0 \end{cases}$.
(2) Two real numbers $(m, n)$ are randomly chosen from the interval $[1, 6]$. Find the probability that the equation $x^2 + mx + n^2 = 0$ has real roots.

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