If $\pi=3.1415926...$, what is the exact value of $|\pi-3.14|+|\pi-\frac{22}{7}|$? Express your answer as a common fraction.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $\pi=3.1415926...$, what is the exact value of $|\pi-3.14|+|\pi-\frac{22}{7}|$? Express your answer as a common fraction.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{350}
If $\pi=3.1415926...$, what is the exact value of $|\pi-3.14|+|\pi-\frac{22}{7}|$? Express your answer as a common fraction.
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