Translation of "Undertook" in French

I undertook responsibility for him.

J'ai assumé la responsabilité à sa place.

If he had any friends or any credit, we undertook that he should lose them.

S'il avait le moindre ami ou crédit, nous entreprîmes de les lui faire perdre.

Tom and Mary then found themselves side by side at the start of this sentence and undertook to explore it.

Tom et Mary se retrouvèrent alors côte à côte au début de cette phrase et entreprirent de l'explorer.