
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 $f(x)=\ln x- \frac {a}{x}$, $g(x)=f(x)+ax-6\ln x$ ($a\in\mathbb{R}$),
(I) Discuss the monotonicity of $f(x)$;
(II) Let function $h(x)=x^{2}-mx+4$, when $a=2$, if $\exists x_{1}\in(0,1)$, $\forall x_{2}\in[1,2]$, such that $g(x_{1})\geqslant h(x_{2})$ holds, find the range of the real number $m$.

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