The preferred method of assessing a patient's responsiveness is through the use of verbal stimulus. This approach is generally favored because it allows the healthcare provider to gauge the patient's cognitive function and ability to respond to communication. When a provider speaks to the patient or calls their name, they can observe whether the patient responds verbally or through intentional movements. This technique is non-invasive and can quickly assess the neurological status without causing discomfort or distress to the patient. Other methods, while useful in specific circumstances, may not provide the same level of insight into responsiveness. For instance, observing breathing can show whether the patient is alive and breathing adequately, but it does not directly indicate how responsive the patient is. Similarly, physical stimulus, such as shaking or applying pressure to the patient, can elicit a response but may also cause additional discomfort or pain, which is less ideal in a clinical assessment of responsiveness. Checking the pulse on a limb primarily assesses circulation and does not effectively gauge a patient's responsiveness. Therefore, the use of verbal stimulus stands out as the method that best assesses a patient's alertness and reaction capabilities.