
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 $b$ and $c$ be the outcomes of rolling a die consecutively.
(1) Let $A = \{x | x^2 - bx + 2c < 0, x \in \mathbb{R}\}$, find the probability of $A \neq \emptyset$;
(2) Let the random variable $\xi = |b - c|$, find the distribution of $\xi$.

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