
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
Given the planar region $\Omega=\{(x, y) \mid x+y \leqslant 6, x \geqslant 0, y \geqslant 0\}$, and another region $A=\{(x, y) \mid x \leqslant 4, y \geqslant 0, x-2 y \geqslant 0\}$, determine the probability that a randomly chosen point within the region $\Omega$ falls within region $A$.

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