Turing machine with possible transitions to the final state Let's say we want to draw the transition graph of a Turing Machine that accepts that language L and then write the sequence of moves done by the TM when the input sequence is $w = abbcbba$ so I had some thoughts on how this could be built.

$q0 - q1: a,a,R$

$q1-q2: b,b,R$

$q2 (loop): b,b,R$

$q2-q3: c,c,R$

$q3-q4: b,b,R$

But then I'm getting stuck here, I could see $b,b,R$ to the final state and then add a separate node to account for the case $m=3$, but I'm teaching this to myself so maybe someone can step in here and get me back on track.

EDIT:

This might work:
I would define F(set of final states)={$q_4,q_5,q_6$} then:

$ q_4-q_5:b,b,R$

$q_4-q_7:X,X,R$ for X=a,c

$q_5-q_6:b,b,R$

$q_5-q_7:X,X,R$ for X=a,c

$q_6-q_7:X,X,R$ for X=a,b,c