
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 $f(x)=(2-a)\ln x+\frac{1}{x}+2ax (a\in R)$,

(I) Discuss the monotonicity of the function $f(x)$;

(II) If for any $a\in (-3,-2)$, ${{x}_{1}},{{x}_{2}}\in [1,3]$, the inequality $(m+\ln 3)a-2\ln 3 > \left| f({{x}_{1}})-f({{x}_{2}}) \right|$ always holds, find the range of values for the real number $m$.

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