LBA for $L = \{a^nb^{2n} \mid n\geq1 \}$

I want to construct a linear bounded automata for the language $L = \{a^nb^{2n} \mid n\geq1 \}$ . I know how LBA works but I don't have an idea how it can count the numbers of a's and check if the b's are 2 times more than a's. I would like to to hear some suggestions.

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Repeatedly remove an $a$ from the beginning and a $bb$ from the end until the string becomes empty. If you cannot do it at any point, reject, otherwise, accept.