
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 an inequality in the form $(m-3) x^{2}-2 m x-8>0$ with respect to $x$, its solution set is an open interval. Furthermore, the length of this interval $l$ satisfies $l \in [1,2]$. Find the range of the real number $m$. (Note: The length of an open interval $(a, b)$ is $l = b - a$.)

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