After administering an injection using a syringe with a safety needle, which action should the nurse take to most effectively prevent a needlestick injury?

Detach the needle from the syringe by hand, then place the needle and syringe separately into the sharps container.

Place the uncapped needle on a tray nearby to recap later when time permits.

Engage the safety device on the needle immediately and dispose of the syringe in a puncture-proof sharps container immediately after use.

Recap the needle carefully using both hands before disposing of it to avoid accidental sticks.