STEP scaffolds force a result early precisely so you can deploy it later. Treat any proved lemma, bound or identity as a reusable instrument: re-substitute specific values, specialise variables, or apply it to a new tuple to clear the next part almost mechanically. If a later part looks intractable, ask which earlier result it is begging you to plug in.
Trigger: the words "hence", "deduce", "use the result above", or a part that mirrors the previous one with different inputs.
Instances:
(i) feed a special value into a just-proved inequality to chain to a stronger bound.
(ii) apply a proved identity to a cleverly chosen new tuple (e.g. a substitution d+e=c, or averaged terms bi).
(iii) reuse a closed form recursively (build the odd case from the even case).
