Multiline equation with lots of texts

How can I replicate this multiline math sentence? (It describes a Turing Machine). It has multiple lines, plain text and I want to align the numbered steps.

$N= "\"On input" x: \
1. "Compute" f(w). \
2. "Run" M "on input" f(w) "and output whatever" M "outputs."\"$

It can be done using & for alignment - and for alignment I’d default to a display equation (the $ ... $ kind of equation), but both kinds work.

$ N= “&"On input" x: \
      & 1. "Compute" f(w). \
      & 2. "Run" M "on input" f(w) "and output whatever" M "outputs."” $

and to fix the spacing of the : you can do this:

#let normal = math.class.with("normal")
// use `normal(:)` in the equation