
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
Given the set $A = \{-9, -7, -5, -3, -1, 0, 2, 4, 6, 8\}$, in the Cartesian coordinate system, the coordinates of point $(x, y)$ satisfy $x \in A$, $y \in A$, and $x \neq y$. Calculate:

$(1)$ The probability that point $(x, y)$ is not on the $x$-axis;

$(2)$ The probability that point $(x, y)$ is exactly in the second quadrant.

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