An indicative or subjunctive question

[LearningSpanish]

Hi guys just wanted to run a sentence by you please :)

I was looking for a good argument to prove that I was right but couldn't find any.

My attempt:

Estaba buscando un buen argumento para demostrar que tenía razón, pero no pude encontrar ninguno.

or should it be

que tuviera razon?

[aleCcowaN]

Estuve buscando un argumento para demostrar que tenía razón, pero no encontré ninguno.

"que tuviera razón" would only be an adjective qualifying "argumento para demostrar", which is grammatically correct but not from the point of view of meaning.

[LearningSpanish]

ok thanx :) sometimes I overthink these things lol