
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 sets $A=\left\{ x\mid x^2+3x-4 < 0 \right\}$ and $B=\left\{ x\mid \frac{x+2}{x-4} < 0 \right\}$,

(1) Find the probability of $x\in A\cap B$ when a real number $x$ is randomly chosen from the interval $(-4,5)$;

(2) Let $(a,b)$ be an ordered pair of real numbers where $a$ and $b$ are integers randomly chosen from sets $A$ and $B$, respectively. Find the probability of $a-b\in A\cup B$.

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