
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
Roll a die twice in succession, observing the upward facing number of points each time, and calculate:
(I) The probability that the sum of the two numbers is 5;
(II) If the upward facing number of points of the first roll is denoted as the x-coordinate, and of the second roll as the y-coordinate to form a point (x, y), find the probability that this point lies within the region Ω defined as:
$$
\begin{cases}
x>0 \\
y>0 \\
x-y-2>0
\end{cases}
$$

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