
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 event A be "The line $ax - by = 0$ intersects with the circle $(x - 2\sqrt{2})^2 + y^2 = 6$."
1. If a die is rolled twice successively and the numbers obtained are denoted by $a$ and $b$, respectively, find the probability of event A occurring.
2. If the real numbers $a$ and $b$ satisfy $(a - \sqrt{3})^2 + (b - 1)^2 \leq 4$, find the probability of event A occurring.

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