
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 $f(x)= \begin{cases} (x-a)^{2}-1,x\geqslant 0 \\ -(x-b)^{2}+1,x < 0 \end{cases}$, where $a$, $b\in R$.
(I) When $a < 0$ and $f(x)$ is an odd function, find the expression of $f(x)$;
(II) When $a > 0$ and $f(x)$ is monotonically decreasing on $(-1,1)$, find the value of $b-a$.

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