Culminating actions (llegar a, acabar por)

Managing to reach an agreement

When someone finally succeeds at doing something after a long process or a lot of effort—meaning "to manage to" or "to come to" do something—use llegar a followed by an infinitive.

The mediator came to understand the dispute.
El mediador llegó a entender la disputa.
The majority of the countries managed to establish a lasting dialogue without hostility.
La mayoría de los países llegaron a establecer un diálogo duradero sin hostilidad.

Ending up with a result

To express that someone "ended up" doing something as the culmination of a situation, use terminar por or acabar por followed by an infinitive. They mean exactly the same thing and are used interchangeably.

The diplomats ended up prolonging the dispute, which frustrated everyone.
Los diplomáticos terminaron por prolongar la disputa, lo que frustró a todos.
However, the president ended up compromising and making a concession.
Sin embargo, el presidente acabó por transigir y hacer una concesión.

Culminating actions in other tenses

Because llegar, terminar, and acabar act as the main verbs in these phrases, you can conjugate them in any tense or mood the sentence requires, including the future tense or the subjunctive.

We will never manage to have a lasting peace if you do not want to compromise.
Nunca llegaremos a tener una paz duradera si tú no quieres transigir.
I doubted that the enemy would end up yielding without any concession.
Dudaba que el enemigo terminara por transigir sin ninguna concesión.