
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
Let \( P\left(x+a, y_{1}\right), Q\left(x, y_{2}\right), R\left(2+a, y_{3}\right) \) be three distinct points on the graph of the function \( f(x)=\log _{2}(x-a) \), and they satisfy the condition \( y_{1}+y_{3}=2y_{2} \). There is exactly one real value of \( x \) that meets this condition. Find the range of the real number \( a \).

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