
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 $f(x) = \frac{\ln(2x)}{x}$.
(I) Find the minimum value of $f(x)$ in the interval $[1,a]$ where $a > 1$.
(II) If the inequality $f^2(x) + mf(x) > 0$ has only two integer solutions for $x$, find the range of the real number $m$.

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