
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
The plane region determined by the system of inequalities 
\[
\begin{cases} 
& x\leqslant 0\,, \\
& y\geqslant 0\,, \\
& y-x-2\leqslant 0\,, 
\end{cases}
\]
is denoted as \({\Omega_1}\), and the plane region determined by the system of inequalities 
\[
\begin{cases} 
& x+y\leqslant 1\,, \\
& x+y\geqslant -2\,, 
\end{cases}
\]
is denoted as \({\Omega_2}\). If a point is randomly selected within \({\Omega_1}\), the probability that this point is exactly within \({\Omega_2}\) is _________.

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