
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 fair die is rolled twice, and the scores obtained are denoted as $m$ and $n$, respectively.
1. Let vector $\overrightarrow{a} = (m, n)$, and vector $\overrightarrow{b} = (2, -2)$. Define event $A$ as $\overrightarrow{a} \cdot \overrightarrow{b} > 0$. Calculate the probability $P(A)$.
2. Calculate the probability that point $A(m, n)$ falls within the region $x^2 + y^2 \leq 16$.

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