Problem analysis ends when you understand a problem well enough to start trying to solve it.
Since designers generally solve the problems of other people, it is vital that the designer understand the problem from the other's point of view.
A product requirements specification (aka requirements set, or design brief) is a record of the agreement between designers and users/clients on the nature of the problem to be solved.
The question is: How can one extract the real problem from the users/clients?
The users/clients may not really know what they want.
Knowing what's wrong implies that you would know when it was right - or at least better.
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