Bug-tracking systems are different than ticket systems. If you have only occasional bugs (maybe your group doesn't write a lot of code) then filing help tickets for yourself is sufficient.
However if your team is serious about writing code, start a separate bug-tracking system. Bug-tracking systems have a different workflow than request ticket systems. Ticket systems are a communication tool between you and your users. Bug-tracking systems track the bug lifecycle (report, verify, assign, fix, close, verify).
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