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The carbon (in coke) burns to form carbon dioxide

carbon + oxygen → carbon dioxide

C(s) + O₂(g) → CO₂(g)

Carbon dioxide reacts with more carbon to form carbon monoxide.

carbon dioxide + carbon → carbon monoxide

CO₂(g) + C(s) → 2CO(g)

The carbon monoxide is the reducing agent which reduces iron(III) oxide to iron.