Criminal procedure principles in relation to Officer Smith scenario

This is an assignment that describes the criminal procedure principles in relation to Officer Smith scenario. Additionally, the paper identifies the legal basis that were for the action.

Criminal procedure principles in relation to Officer Smith scenario

Please write a 3 to 5 page (in total), double-spaced paper on the following two questions:
1.    Officer Smith is on routine patrol when he sees a car driving with a broken tail light.  Officer Smith activates his emergency equipment and pulls the car over.  As Officer Smith approaches the car, he realizes that the tail light is not broken.  However, he notices that the car is a four door blue Ford Focus with a dent on the rear driver’s side of the car and that the only occupant is the white male driver.  Officer Smith realizes that the car matches the description of a car used in an armed robbery that had occurred minutes earlier.  The officer had heard the description broadcast over his police radio.

Officer Smith orders the driver, Peter Parker, to step out of the car.  Officer Smith conducts a pat down of Parker, and feels what he believes to be a gun in Parker’s pants pocket.  Parker suddenly runs away from Officer Smith.  Officer Smith chases Parker and catches him.  Officer Smith handcuffs Parker and searches his pockets.  The officer finds a loaded 9 mm handgun in his pocket.  Subsequently, officer Smith returns to Parker’s car and searches it.  During the search, Officer Smith finds a diamond ring and a ruby necklace in the trunk.  Subsequent investigation reveals that these items were taken during the armed robbery.
Taking his actions, step by step, analyze whether Officer Smith’s actions were reasonable under the Fourth Amendment.  Start with the initial traffic stop and end with the arrest.

Was there a legal basis for each of his actions? Explain the legal principles involved.