No, not how it works. You can flash a few times and go semi AFK, done it myself plenty of times in low level dungeons.
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Even during early progression you will find windows to DPS.
Basically you DPS whenever you would be standing around doing nothing. The better your group gets at a fight, the more you would stand around twiddling your thumbs. Filling that space with damage casts is the logical thing to do.
No one expects you to DPS when heal is needed. They merely expect you to not stand around doing NOTHING while waiting for some damage to come in. ESP in dungeons. Ugh. I don't get it how players manage to stand around looking dumb 75% of the time.
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Was in Pagos yesterday. 14 whopping people.
Yeah I guess no relic for me.