
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 $f(x)=|x-1|+|x+a|$,  
(I) when $a=3$, solve the inequality $|x-1|+|x+a| > 6$ with respect to $x$.  
(II) If the function $g(x)=f(x)-|3+a|$ has a zero, find the range of the real number $a$.

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