
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) = $$\begin{cases} \overset{-x^{2}+ax+a+1,x\leq 1}{ax+4,x>1}\end{cases}$$, find the range of values for the real number a such that there exist x₁, x₂ ∈ R, and x₁ ≠ x₂, for which f(x₁) = f(x₂) holds true.

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