<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def process_result(self, new_sia, min_sia):
 """Check if the new SIA has smaller |big_phi| than the standing result. """

        if new_sia.phi == 0:
            self.done = True  # Short-circuit
            return new_sia

        elif new_sia < min_sia:
            return new_sia

        return min_sia