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First, maintain composure and avoid forcing it further. Inspect the key to see if enough material remains exposed for extraction. Use pliers or tweezers to grasp and gently pull out the broken piece if possible. Lubricate the keyhole with a graphite-based spray to aid removal. If self-removal proves challenging or risks damaging the lock, seek a professional locksmith's assistance. They possess the necessary tools and expertise to extract the key without causing damage.

If you also have a standard door leading to your garage, install a robust deadbolt lock and reinforce the frame with security plates. Then, secure any windows with shatterproof glass or film to deter break-ins. Consider a smart garage door opener for your car entrance, enabling remote monitoring and control through your smartphone. Motion-activated lighting around the garage to deter intruders is a great way to amplify these security efforts. Lastly, educate your family on security practices, such as keeping the garage entrances closed and locked.

It could be difficult to get in and out of a lock for several reasons, such as the keyhole needing additional lubrication. Particles, debris, and dirt can also get into a lock, making a key stuck (the lubrication can help with the removal). 

Regrettably, entirely pick-proof locks don't exist unless you opt for keyless varieties. Locks advertised as "pick-proof" are, in reality, more resilient against lock-picking and bumping attempts because of complex mechanisms consisting of pins and sidebars. These locks work like this—they assign two tasks to the key, enhancing security by making unauthorized entry more challenging.