For a Turing Machine M below,

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$(1)[5]$ Give a language L$($M$)$ that is recognized by M in the formal definition $($including a regular expression$).$

$(2)[5]$ By reviewing the transitions of TM$,$ give a grammar for L$($M$).$

Hint: L$($M$)$ is a regular language.

$(3)[5]$ Give a derivation for $01011010$ using the grammar in $(2).$