It's a phrase often used in legal or philosophical contexts to emphasize the importance of basing actions and decisions on truth and honesty.
Here are some examples of how it might be used:
* "Il est important d'agir ensuivant la vérité, même si cela est difficile." (It is important to act in accordance with the truth, even if it is difficult.)
* "Le juge a rendu son verdict ensuivant la vérité, après avoir examiné toutes les preuves." (The judge delivered his verdict in accordance with the truth, after having examined all the evidence.)
Let me know if you have any other questions!