
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 functions f(x) and g(x), let a ∈ {x | f(x) = 0} and β ∈ {x | g(x) = 0}. If for all α and β, |α - β| ≤ 1, then f(x) and g(x) are called "adjacent zero-point functions". If f(x) = x - 1 and g(x) = x^2 - ax - a + 3 are "adjacent zero-point functions", find the range of values for the real number a.

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