
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]


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Given the plane region $\Omega=\{(x,y)|x > 0, y > 0, x+y < 2\}$, $A=\{(x,y)|x < 1, y < 1, x+y > 1\}$. Calculate the probability of a point $P$ falling into region $A$ when $P$ is randomly placed within the region $\Omega$.

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