
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
A two-dimensional ordered array $(x,y)$ is generated randomly by a computer, where $-1 \leqslant x \leqslant 1$ and $-1 \leqslant y \leqslant 1$.
(1) If $x$ and $y$ are integers, find the probability of the event "$x^{2}+y^{2} \leqslant 1$".
(2) Find the probability of the event "$x^{2}+y^{2} > 1$".

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