
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
Let set $A=\{(x,y) \,|\, |x|+|y| \leq 2\}$, and $B=\{(x,y) \in A \,|\, y \leq x^2\}$. Calculate the probability that a randomly selected element $P(x,y)$ from set $A$ belongs to set $B$.

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