The headword, presumably extracted from the quotation given, is the aorist subjunctive middle, third person plural, of the verb proi/hmi, I send beforehand, let go, give away, but in the middle voice also I abandon, desert; see generally LSJ s.v. B.II.2.
[1] The first glossing verb is the future indicative active, third person plural (with nu movable), of the verb prodi/dwmi; cf. the aorist infinitives of the headword and this gloss at pi 2394, Synagoge s.v. proe/sqai, and see generally LSJ s.v. The second glossing verb is the same form but from the verb a)mele/w; see generally LSJ s.v.
[2] Cassius Dio 68.11.2 (where the verb is accented prow=ntai: web address 1). The passage describes the political and military strife instigated in the summer of 103 CE by Decebalus (Dekebalos, ruled 85-106 CE; cf. delta 189, delta 344, and OCD(4) s.v.), king of Dacia (Dakia, lower Danube region; cf. delta 23 and OCD(4) s.v. Dacia; Barrington Atlas map 21 grids E-F4), often thwarting Trajan (Roman emperor 98-117 CE; cf. tau 902 and OCD(4) s.v.); Seton-Watson, p. 2. The quotation is also given by Constantine Porphyrogenitus, Excerpta de Legationibus 427.16. [In her critical apparatus Adler notes that mss GM omit o(/ti: that.]