To determine the correct temperature the soup must reach in the next four hours for it to be properly cooled, we reference the standard food safety guidelines for cooling hot foods. These guidelines typically state that hot foods should be cooled from:
1. 135°F (57°C) to 70°F (21°C) within two hours
2. 70°F (21°C) to 41°F (5°C) within an additional four hours
Given that the large pot of soup has already been safely cooled to 70°F (21°C) within the initial two hours, the next step is to cool it further within the remaining four hours.
Following this guideline, the soup must be cooled to 41°F (5°C) in the subsequent four-hour period.
Thus, the correct answer is:
a. [tex]$41^{\circ} F \left(5^{\circ} C\right)$[/tex]