I have learnt that we can use a 普通形 before ため but I don't know whether the tense in 普通形 should agree with the tense in the main clause or not.
Thanks a lot.
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The Japanese language is based on relative tense.
A ため-clause must be in the past tense if it describes a cause/reason that happened in the past in relation to the main clause.
A ため-clause must be in the present tense if it describes the purpose of the main clause (because the ため-clause describes something in the future in relation to the main clause).
Even if you are talking about what you did yesterday, you have to use 見る before ため. 映画を見たために家を出ました is at least grammatical, but it would sound like "I left home because I had watched a move", which usually makes little sense.