
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 $$f(x)= \frac {x+a}{x+b}$$ (where $a$ and $b$ are constants),
(I) If $b=1$, solve the inequality $f(x-1) \leq 0$;
(II) If $a=1$, find the range of $b$ such that for all $x \in [0, 1]$, the inequality $$f(x) > \frac {-1}{(x+b)^{2}}$$ always holds.

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