What do engineers do when they research a problem?

One sapproach is to follow the scientific method of the PDCA (plan, do, check, adjust) cycle.

In the Plan stage:

First & foremost they must fully understand the problem, i.e. they must be able to "grasp the situation". A problem is a deviation from a standard. They must first define the problem adequately. From there, they must move on to gather data to understand root causes of the problem, then prioritize them based on highest to lowest significance & finally hypothesize solutions that will resolve the issues causing the problem. This makes up the PLAN phase In the DO, Check, & Adjust phases:

They are following a feedback loop cycle to ensure that the hypothesized solutions indeed address the root causes to the problem. If so, they must standardize these solutions, if not, they must go back to PLAN.