
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 a point P is randomly selected within the plane region $\{(x, y) | y \leq -x^2 + 2x, \text{ and } y \geq 0\}$, the probability that point P is exactly within the plane region $\{(x, y) | y \leq x, x + y \leq 2, \text{ and } y \geq 0\}$ is \_\_\_\_\_\_.

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