I currently have these two equations, but they are too long to fit on one line:

\begin{align*} [((a_0, a_1, a_2)+(b_0, b_1, b_2)) + (c_0, c_1, c_2)] &= [((a_0 + b_0, a_1 + b_1, a_2 + b_2)) + (c_0, c_1, c_2)] \\ &= (a_0 + b_0 + c_0, a_1 + b_1 + c_1, a_2 + b_2 + c_2) \\ \end{align*}

I want to achieve something to this effect:

I have tried using the split environment within the align environment, but that doesn't allow me to align the line breaks, while also keeping the equal signs independently aligned. I am also open to alternative ideas on how to make this look better. (I do not think the second equality looks great in my mockup.)

I currently have these two equations, but they are too long to fit on one line:

\begin{align*} [((a_0, a_1, a_2)+(b_0, b_1, b_2)) + (c_0, c_1, c_2)] &= [((a_0 + b_0, a_1 + b_1, a_2 + b_2)) + (c_0, c_1, c_2)] \\ &= (a_0 + b_0 + c_0, a_1 + b_1 + c_1, a_2 + b_2 + c_2) \\ \end{align*} 

I want to achieve something to this effect:

I have tried using the split environment within the align environment, but that doesn't allow me to align the line breaks, while also keeping the equal signs independently aligned. I am also open to alternative ideas on how to make this look better. (I do not think the second equality looks great in my mockup.)