
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
There are four balls in a bag, each identical in shape and size but numbered 1, 2, 3, and 4.
(I) A ball is randomly drawn from the bag, and its number is noted as $a$. Then another ball is drawn from the remaining three balls in the bag, and its number is noted as $b$. Find the probability that the quadratic equation $x^2 + 2ax + b^2 = 0$ has real roots.
(II) A ball is drawn at random from the bag, and its number is designated as $m$. After placing it back into the bag, another ball is drawn at random, and its number is designated as $n$. If the coordinates of point $P$ are considered to be $(m, n)$, find the probability that point $P$ lies within the region defined by the inequalities:
$$
\begin{cases}
x - y \geq 0 \\
x + y - 5 < 0
\end{cases}
$$

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