Step 1: Identify all the events and times mentioned in the input text and compile them into a list.
Step 2: Identify the specific question asked about the time range for James or Sarah to have gone to a specific place.
Step 3: Create a timeline starting from the earliest event (waking up) to the latest event (closing time of the place).
Step 4: Place each event on the timeline according to the given time range. Output the timeline with events placed accordingly.
Step 5: Identify the time range for the specific place (beach, amusement park, clothing store) based on the events mentioned. Output the possible time range for James or Sarah to have gone to that place.
Step 6: Compare the possible time range with the options provided. Output the comparison results for each option.
Step 7: Select the option that matches the deduced time range based on the events. This is the answer to the question. Output the selected option as the solution to the task.