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To clarify your rotation it's better to see it as a priority list which is always as follow:
1) Flame Orb
2) Living Bomb
3) Pyroblast from proc
Use combustion with reasonable ignites (this depends on your toon and gear) and scorch while moving.
AOE is situational. The best aoe is spreading combustion so if you need to do aoe damage fast try to plan for this. After that it will depend on number of targets. In general what I do is if there are more than 5 targets I Flame blast then flamestrike spam. This will eat mana so you must also take that into consideration. If there are 4 or less targets I keep living bomb up on each and keep a regular rotation spreading all ignites with impact procs. My gear has me at about 32K single target dps and by spreading ignites I will do around 40K dps; spreading combustion can bring this number up to 70K for the duration and Blast wave/flamestrike on multiple targets is about 50K. (yoshr adds for example)
With your gear you should be doing closer to 30k dps so you're biggest problem is likely just not enough casting. To increase your dps ask yourself if there was any possible way you could've gotten more casts off in an encounter. Since we can cast while moving, this means that if you're not on GCD or casting at any time during the fight; there is room for improvement. We can have 100% active times; moving is no excuse for us to not be dpsing.
Hope this helps.
It's also good to note that any Fire mage should start off with Scorch, unless you have a demo/destro warlock or similar class that gives the 5% crit debuff.
However, I don't really agree with the AoE dps given above. Spamming flamestrike is useless, you only want to put another flame strike down after your previous one has faded. If you're ever dealing with AoE, your best bet is to impact whichever dots you have on your main dps target. Obviously if you can impact a combustion that will give you the biggest dps, but if you dont have combustion up, impacting ignite/LB/Pyro will still deal a considerable amount of damage.
When the adds start coming in, ie. yorsahj black blood adds start spawning, try to get the best ignite you can, and keep your other dots up, hopefully you get an impact proc to just impact everything off to the adds. Once they are grouped up hit everything with a blastwave for blastwave damage + flamestike (assuming you're specced into it). If you didn't have an impact proc prior, blastwave is also a great way to fish for an impact proc. If blastwave still leaves you with no impact proc, line up a dragon's breath to hit everything and hopefully that will give you an impact proc. If you're still left without an impact proc at this point, if the adds still have a decent amount of health, you're left with 2 options. You can either refresh your dots via single target dps on your main target, and blast wave again once it comes off cooldown, or you can arcane explosion spam to fish for an impact proc then refresh your dots and impact them off.
Also, as an offtopic question, I've seen contradicting reports as to whether it's better to refresh living bomb prior to it falling off, or to let it fall off and get the explosion damage. I've also heard from some people that even if you refresh it, the explosion will still happen when it would have fallen off, but after testing it on the dummy, I couldn't reproduce this. My gut tells me that if you have multiple mobs it's better to let it fall off and explode then refresh it, vs. single target it would be better to refresh it.
It's also worth mentioning that there are many times in a single dps priority where it falls off anyway, right at the end of a fireball cast, etc. and then is refreshed upon GCD cooldown. Does anyone have any more insight into this?