
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 $f(x)$ is an increasing function defined on $(0, +\infty)$ and satisfies $f\left(\frac{x}{y}\right) = f(x) - f(y)$.  
(I) Find the value of $f(1)$.  
(II) Solve the inequality: $f(x-1) < 0$.

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