
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 $f(x) = |x-a| - \frac{1}{2}x$ with $a > 0$:  
(I) If $a=3$, solve the inequality $f(x) < 0$ with respect to $x$;  
(II) If for any real number $x$, the inequality $f(x) - f(x+a) < a^2 + \frac{a}{2}$ always holds, find the range of the real number $a$.

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