Some verbs do not take -ado or -ido at all. These five are the ones to know, and each doubles as an adjective in the usual way.
Dicho and hecho are nice to learn together, since both take that /ch/ sound. Abrir has no h, despite the sound.
Lo he roto · Los he roto · Se ha roto · Está roto · Está rota · Ha muerto · Está muerto · Lo he abierto · Están abiertos · Lo he dicho · Le he dicho · Lo he hecho · Está hecho
You have seen a verb's noun hiding in the "to" form and the "I" form. Here it is in the after-haber form.
You will see hecho en China, made in China, on products, which is a good reminder of the adjective.
Hecho and fact look unrelated, but they are not. In a phonetic change in Spanish, many f's became silent h's. English fact comes from the same root as faire, to do, exactly as hecho comes from hacer.
You can even see it inside Spanish itself: hierro is iron, and ferrocarril is railways. They look unrelated until you know the f became a silent h and the e split into ie.
Combine the -ía forms with haber in its "to" form.
Debería haber cancelado · Lo debería haber cancelado / Debería haberlo cancelado · Podría haber ido · Podríamos haber ido · Debería haberlo hecho · Deberías haberlo hecho
Because haber is in the "to" form, the little word can attach to its end.
Some of these adjectives can take ser. Complicado works with either, and you may feel drawn to one or the other depending on what you are talking about. But muerto never takes ser.
Es complicado / Está complicado · but only está muerto
Estoy muerto is also commonly used to mean I'm exhausted. And me muero, I'm dying, gets used constantly: from embarrassment, from laughter, from disbelief.
You can see the e splitting between festival and fiesta.
Está cancelado · Está cancelada · Se ha complicado (it has got complicated)
With morir you will hear both ha muerto and se ha muerto, with little difference.