
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 $f(x)=(x-2)\ln x+2x-3$, $x\geqslant 1$.

(I) Determine the number of zeros of the function $f(x)$.

(II) If the function $g(x)=(x-a)\ln x+\frac{a(x-1)}{x}$ is an increasing function on $[1,+\infty)$, find the maximum value of the integer $a$.

(You might need the following data: $\ln 1.59\approx0.46$; $\ln 1.60\approx0.47; \frac{400}{41}\approx 9.76$)

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