
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 $x=1$ is an extreme point of the function $f(x)=2x+\frac{b}{x}+\ln x$,
(I) Find the value of $b$;
(II) Find the interval where the function $f(x)$ is decreasing;
(III) Let $g(x)=f(x)-\frac{3}{x}$, how many tangent lines can be drawn from the point $(2,5)$ to the curve $y=g(x)$? Please explain your reasoning.

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