Final answer:
The most critical assessment indicating the need for rapid action in a patient with a head injury is difficulty in arousing the patient, as it suggests a possible escalation in the severity of their condition.
Step-by-step explanation:
When caring for a patient who has had a head injury, the assessment information that requires the most rapid action by the nurse is that the patient is more difficult to arouse. This change in level of consciousness could indicate an escalation in the severity of the patient's condition, such as increased intracranial pressure or a worsening brain injury, making it a critical sign that immediate medical intervention may be necessary. Other assessments such as a slight irregularity in pulse, an increase in blood pressure, and the patient's complaint of a headache, although important, do not suggest as immediate a threat to the patient's condition as a decreased level of consciousness does.