
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 that the inequality \(\left[\left(\log _{3} m\right)^{2}-\log _{3}\left(27 m^{2}\right)\right] x^{2}-\left(\log _{3} m-3\right) x-1<0\) holds for all real numbers \(x\), find the range of the real number \(m\).

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