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I'm dieting to lose weight, but what types of exercise should I do to accompany my diet?

It's great that you're asking about exercise that will accompany your diet - they're both equally important to reach your goals!  There are three parts to a good exercise program: cardiovascular, strength and flexibility.  
The question is - have you been exercising in the past, or are you just starting out?  If you're just starting out you'll want to ramp it up slow.  If you've been exercising you'll want to increase your intensity. Read more here: