
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
Determine the values of the variable \( x \) such that the four expressions \( 2x - 6 \), \( x^2 - 4x + 5 \), \( 4x - 8 \), and \( 3x^2 - 12x + 11 \) differ from each other by the same constant amount, regardless of the order of the expressions. Find all possible integer values of \( x \).

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