
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 parabola $y=ax^{2}+bx+c$ ($a\neq 0$) with its axis of symmetry to the left of the $y$-axis, where $a$, $b$, $c \in \{-3,-2,-1,0,1,2,3\}$, let the random variable $X$ be the value of "$|a-b|$". Then, the expected value $EX$ is \_\_\_\_\_\_.

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