
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 $f(x)=mx-\frac{m-1}{x}-\ln x$, where $m\in R$. The function $g(x)=\frac{1}{x\cos \theta}+\ln x$ is increasing on $[1,+\infty)$, and $0\in[0, \frac{\pi}{2})$.
(I) Find the equation of the tangent line to $f(x)$ at point $P(1,f(1))$ when $m=3$.
(II) Find the possible values of $\theta$.
(III) If $h(x)=f(x)-g(x)$ is monotonic on its domain, find the range of possible values for $m$.

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