
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
In the interval $\left[-2,3\right]$, a number $m$ is randomly chosen. The probability that the eccentricity of the hyperbola $\frac{{x}^{2}}{{m}^{2}-1}-\frac{{{y}^{2}}}{4-m}=1$ is greater than $\sqrt{3}$ is given by the ratio of the length of the interval for which the eccentricity is greater than $\sqrt{3}$ to the total length of the interval.

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