How to covert full length AR-15 to carbine length?

I was thinking about converting my .223 Colt AR-15 from a full length barrel (20in) to a carbine length barrel (14.5in) to optimize maneuverability and reduce overall weight. Obviously I need a new barrel and handguards, but I assume I also need a new gas system. The gas system I've never messed with so any... show more I was thinking about converting my .223 Colt AR-15 from a full length barrel (20in) to a carbine length barrel (14.5in) to optimize maneuverability and reduce overall weight. Obviously I need a new barrel and handguards, but I assume I also need a new gas system. The gas system I've never messed with so any input would be appreciated.

It has a fixed front sight about 6.5in away from the end of the muzzle brake. I see the gas tube begin about 8.5in from the end of the muzzle brake (the front sight being 2in wide). The visible portion of the gas tube is 11.5in from the front sight to the delta ring.

I would just get a new carbine, but they're all currently sold out and being price gouged anyway.
Update: Just for clarification, I'm not cutting the barrel or any parts. I would order a new barrel and gas system and replace them myself.
Update 2: I'm currently under Colorado law, so no issues with this.
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