
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) = $$\begin{cases} (2b-1)x+b-1, & x>0 \\ -x^{2}+(2-b)x, & x\leq 0\end{cases}$$, find the range of values for b such that for any x₁ ≠ x₂, the inequality $$\frac {f(x_{1})-f(x_{2})}{x_{1}-x_{2}}$$ > 0 holds true.

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