
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) Toss a die (a cube marked with 1, 2, 3, 4, 5, 6 on its faces) twice in succession, and use the numbers $(m,n)$ obtained to represent the coordinates of point $P(m,n)$. Calculate 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) Randomly select two real numbers $(m,n)$ within the interval $[1,6]$, and calculate 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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