
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 $f(x) = \frac{2(x-a)}{x^2+bx+1}$ is an odd function.  
(I) Find the intervals of monotonicity for $f(x)$.  
(II) There exists a solution for the inequality $2m-1 > f(x)$ with respect to $x$, find the range of values for $m$.

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