After να, using the present subjunctive (which looks like the "normal" present indicative tense in modern Greek) generally talks about repeated or habitual things.
Προσπαθεί να πηγαίνει would be something like "he keeps trying to go".
But for a one-time action, you need the aorist subjunctive -- which for πηγαίνω is να πάει.
But isn't πάω the alternative form of πηγαίνω ?
It's the aorist stem used with present meaning.
Or are the present form and the aorist subjunctive indentical here ?
πηγαίνει can be present indicative or present subjunctive.
πάει is basically aorist subjunctive, but it can also be used as present indicative.