
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 a parabola $y = ax^2 + bx + c$ ($a \neq 0$) whose axis of symmetry is located to the left of the y-axis, and where $a, b, c \in \{-3, -2, -1, 0, 1, 2, 3\}$, consider the random variable $\xi$ defined as the value of $|\ a - b|$. Calculate the expected value $E[\xi]$.

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