"I am not sleeping, but reading."
Translation:Nem alszom, hanem olvasok.
Because it's an -ik verb. (The third person singular "he, she, it" form ends in -ik: alszik.)
-ik verbs have (in general) the first person singular indefinite form -em, -om rather than -ek, ok.
Thus dolgozom, alszom, úszom, esem, ....
By the way, how crazy does this "-ik verb" thing sound to non-native Hungarians? Are you people OK with it and just take it in stride? Or is it beyond anything that could reasonably be expected from anyone to learn? :)
It feels pretty tame to me.
French, for example, has verbs in -er, -re, -ir, -oir which all conjugate a bit differently, and the -ir verbs are split up into ones that take an -iss- infix in some forms and verbs that don't (e.g. finir: nous finissons but dormir: nous dormons).
Greek as I learned it has verbs in (unaccented) -ω, in -άω, and in accented -ώ. Plus some verbs that are passive in form but active in meaning such as θυμάμαι "remember" or κοιμάμαι "sleep".
Having Hungarian verbs depend mostly on two things (-ik or not / stem-final sibilant or not for -l vs. -sz) seems pretty straightforward compared to that.
The separate definite/indefinite conjugation, on the other hand, is rather unusual and takes some getting used to. (As do the variant consonant assimilations, both the ones in speech [egészség = egés-ség not egész-ség] and the ones in writing [olvassa rather than olvasja for "he reads it", though the back ending is "normally" -ja, e.g. tudja].)