
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 quadratic equation in terms of $x$: $x^{2}-4x+m-1=0$, where $x_{1}$ and $x_{2}$ are the real roots. If $3x_{1}x_{2}-x_{1}-x_{2} \gt 2$, then the range of $m$ is ______.

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