How will taking away privileges teach this boy anything about taking things that don't belong to him, or the ethics of ownership?
How will writing a paper on this teach him what to do differently next time he takes a mis-step or is tempted by something?
The purpose of these exercises is to punish, not to teach. One unfortunate side effect of punishment is the creation of a deep and lasting desire to avoid getting caught again. Rather than a deep and lasting desire to avoid stealing or lying again, which is supposed to be the point, right?
One power that parents often underestimate is the power of their natural reaction to change a child's behaviour. Your son wants your love and approval, and when he does something like this that is SO far away from getting it, the disappointment in your face speaks volumes. If you let it.
When parents don't trust the power of their natural reaction, and instead seek to control what a child thinks about something, or attempt to 'make him pay' for something that has no real cost associated, they inadvertently step into the role of 'perpetrator'. A minute ago, the boy felt bad about what he'd done, the fact that he'd lied and the complications of getting caught. That could have ended in a powerful lesson... but instead, now he feels oppressed, disliked, tormented and hurt. Now, to him, it's all about how he's a victim --how it's not fair, how you're mean, how no one listens to him. He has been moved from a place where he can regret (and admit regret) about his actions to a place where he must not only defend himself against you, but must continue to deny the actions in order to attempt to regain your love, because clearly stealing=no love.
Parents need to give children room to understand what they've done, space and time to see why we think stealing and lying are wrong --including your real reaction to feeling betrayed and not trusting your child. That is powerful, nearly overwhelming stuff for a child, all by itself. Without the need to staple on anything punitive.
I also believe that what you've asked him to do, and what he's had taken away are disproportional to the 'crime' --first, because it's a first offense (one strike, you're out) and second because it leaves no latitude for when he gets caught dealing drugs or injures someone. What is left to do for something more serious, shoot him?
Above all else, the critical issue for parents is staying in a position of influence in a child's life, as the child navigates the difficult complexities of temptation, unsupervised time, and ethics. To stay in a position of influence, the child must see the parents as 'on his side,' and loving him no matter what he does. The willingness to guide and correct mis-steps and mistakes needs to be something a child can see his parents have... this requires understanding his actions, his thinking and his struggles. Not punishing his actions, his thinking or his struggles.