<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Given the expression:
$$
x = \left(\frac{\sqrt{(a-2)(|a|-1)}+\sqrt{(a-2)(1-|a|)}}{1+\frac{1}{1-a}}+\frac{5a+1}{1-a}\right)^{1988},
$$
find the unit digit of \( x \) when evaluated at suitable values of \( a \). Express your answer as a single digit (0-9) without units or decimal places. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
6
Given the expression:
$$
x = \left(\frac{\sqrt{(a-2)(|a|-1)}+\sqrt{(a-2)(1-|a|)}}{1+\frac{1}{1-a}}+\frac{5a+1}{1-a}\right)^{1988},
$$
find the unit digit of \( x \) when evaluated at suitable values of \( a \). Express your answer as a single digit (0-9) without units or decimal places.
test