
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
The lengths of the intervals $\left(m,n\right)$, $\left[m,n\right]$, $\left(m,n\right]$, and $\left[m,n\right)$ are all $n-m$, where $n > m$. If the sum of the lengths of the solution sets of the inequality system $\left\{\begin{array}{l}{1≤\frac{12}{x+3}≤3}\\{{x}^{2}+3tx-4{t}^{2}＜0}\end{array}\right.$ is $8$, then the range of real number $t$ is ______.

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