The adjective that describes something carefully thought out and formed is "deliberate." When an action is done on purpose or intentionally, it is often referred to as being "deliberate."
As for the verb that means to think or consider carefully, you can use "deliberate" as well. For example, you can say, "He deliberated on the decision for a long time before making a choice."
In summary, when something is described as deliberate, it suggests a sense of intentionality and careful planning. The verb "to deliberate" refers to the act of thinking or considering something with careful attention, typically before making an important decision.