
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
Consider the functions $f(x)=|x-1|$ and $g(x)=2|x+a|$.
(I) When $a=1$, find the solution set for the inequality $f(x)-g(x) > 1$.
(II) If the inequality $2f(x)+g(x) \leqslant (a+1)^{2}$ has a solution with respect to $x$, determine the range of values for $a$.

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