What does a graphic designer need to do to monitor the progress of the project

At first the graphic designer has to break the process down into it's fundamental components. Which could be:

1) Discussion and Clear Comprehension of the Brief

2) Research and Collection of Information

3) Sketching

4) Execution and Experimentation

5) Finalization

6) Revision and Further Corrections

7) Submissions

Then self-analysis is required to figure out the current stage process. Project management soft-wares such as Trello could be helpful when it comes to tracking the progress. Hope this answers the question.

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