
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) = $$\begin{cases} (2-a)x+1 & (x<1) \\ a^{x} & (x\geq 1) \end{cases}$$ which satisfies (x₁ - x₂) • [f(x₁) - f(x₂)] > 0 for any x₁, x₂ where x₁ ≠ x₂, determine the range of values for the real number a.

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