corriésemos
-we ran
The word corriésemos is the imperfect subjunctive form of correr in the first person plural.
See the full correr conjugation

correr

¿No fue también el Consejo de Ministros el que quería tener una AESA independiente, una autoridad cuyas conclusiones fueran fiables, con la que no corriésemos el riesgo de recibir estudios ficticios?
Was it not also the Council of Ministers that wanted to have an independent EFSA, an authority on whose findings you can rely, an authority where there is no risk of getting bogus studies?
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