
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 $S$ be the solution set to the inequality $x^2 - x - 6 \leq 0$. For integers $m, n \in S$,
(1) Denote event $A$ as "the ordered pairs $(m, n)$ such that $m + n = 0$". Enumerate the fundamental events included in $A$.
(2) Let $\xi = m^2$. Calculate the probability distribution of $\xi$ and its expected value $E(\xi)$.

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