Yes both are verbs and both might be simple past in your context. [I guess]
because simple past and past participle have same forms for (hold, greet)
hold = simple present
held = simple past
held = past participle
greet = simple present
greeted = simple past
greeted = past participle
So, held might be simple past in your context.
Similarly greeted also simple past in your context.
I hope other members/moderators will clarify your doubts more clearly.
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