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A mental process or a phenomenon dedicated towards solving problems by discovering and analyzing the problem is referred to as problem-solving. It is a process dedicated to finding not just any solution, but the best solution to resolve any problems. There is no such thing as one best way to solve every kind of problem, since there are unique problems depending upon the situation there are unique solutions too.

In psychology, problem solving doesn’t necessarily refer to solving psychological/mental issues of the brain. The process simply refers to solving every kind of problems in life in a proper manner. The idea of including the subject in psychology is because psychology deals with the overall mental process. And, tactfully using our thought process is what leads to the solution of any problems.
There are number of rigid psychological steps involved in problem solving, which is also referred as problem-solving cycle. The steps are in sequential order, and solving any problem requires following them one after another. But, we tend to avoid following this rigid set of steps, which is why it often requires us to go through the same steps over and over again until a satisfactory solution is reached.

Cite: https://www.psychestudy.com/cognitive/th...em-solving

The Steps in Problem-Solving

In order to correctly solve a problem, it is important to follow a series of steps. Many researchers refer to this as the problem-solving cycle, which includes developing strategies and organizing knowledge.

While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution. Instead, we often skip steps or even go back through steps multiple times until the desired solution is reached.

Identifying the Problem: While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.
Defining the Problem: After the problem has been identified, it is important to fully define the problem so that it can be solved.
Forming a Strategy: The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences.
Organizing Information: Before coming up with a solution, we need to first organize the available information. What do we know about the problem? What do we not know? The more information that is available, the better prepared we will be to come up with an accurate solution.
Allocating Resources: Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is. If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources into coming up with a solution.

Monitoring Progress: Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies.
Evaluating the Results: After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.​

Cite: https://www.verywellmind.com/what-is-pro...ng-2795485

In cognitive psychology, the term problem-solving refers to the mental process that people go through to discover, analyze, and solve problems. This involves all of the steps in the problem process, including the discovery of the problem, the decision to tackle the issue, understanding the problem, researching the available options and taking actions to achieve your goals. Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

There are a number of mental processes at work during problem-solving. These include:

Perceptually recognizing a problem
Representing the problem in memory
Considering relevant information that applies to the current problem
Identify different aspects of the problem
Labeling and describing the problem

Cite: https://www.verywellmind.com/problem-solving-2795008