
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 bag contains four balls of identical shape and size, numbered $1$, $2$, $3$, $4$.
(I) A ball is randomly drawn from the bag, its number recorded as $a$, then another ball is randomly drawn from the remaining three, its number recorded as $b$. Find the probability that the quadratic equation $x^{2}+2ax+b^{2}=0$ has real roots.
(II) A ball is randomly drawn from the bag, its number recorded as $m$, then the ball is returned to the bag, and another ball is randomly drawn, its number recorded as $n$. If $(m,n)$ is used as the coordinates of point $P$, find the probability that point $P$ falls within the region $\begin{cases} x-y\geqslant 0 \\ x+y-5 < 0\end{cases}$.

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