
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 $f(x) = |x-1| + |x+a| - x - 2$.
- (I) When $a=1$, find the solution set of the inequality $f(x) > 0$.
- (II) Let $a > -1$, and there exists $x_0 \in [-a, 1)$ such that $f(x_0) \leq 0$, find the range of $a$.

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