estarían adoptando
-they/you would be adopting
Conditional progressive ellos/ellas/ustedes conjugation of adoptar.

adoptar

No sabía que estarían adoptando.
I didn't knowyou were adopting.
Manifestaron al respecto, que estarían adoptando una serie de acciones que citaron como prueba fehaciente de su implementación por parte del Estado.
In that respect, they stated that they would be adopting a series of actions they said would serve as convincing evidence of its implementation on the part of the State.
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