
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
Generate a binary array in the region $\begin{cases} -1 < x < 1 \ -2 < y < 2 \end{cases}$ using a computer. For each binary array $(x,y)$, use a computer to calculate the value of $x^{2}+y^{2}$. Denote the event "$(x,y)$ satisfies $x^{2}+y^{2} < 1$" as event $A$. The probability of event $A$ occurring is _______.

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