
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 the function $f(x)=3mx- \frac{1}{x}-(3+m)\ln x$, if for any $m\in(4,5)$, $x\_1$, $x\_2\in[1,3]$, the inequality $(a-\ln 3)m-3\ln 3 > |f(x\_1)-f(x\_2)|$ always holds, then the range of the real number $a$ is \_\_\_\_\_\_.

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