Final answer:
The correct word to fill in the blank is 'breach,' which means to forcibly break through an obstacle or barrier such as a gate or door.
Step-by-step explanation:
The police, followed by the curious neighbors, had to breach the front gate and the entry doors to get into the house. This action signifies a forceful entry, typically meaning that the doors or gate had to be broken through.
This term is appropriate in the context given, especially with historical precedences in literature where forceful entries are depicted during heightened scenarios, be it during law enforcement actions or mob riots.
Descriptions of similar acts can be found in tales of tax collector intimidation, where their properties were severely damaged by mobs, or scenes in fiction where characters engage with doors, whether by unlocking, opening, or breaking them to gain access.
Regardless of the era, breaching remains a term commonly associated with the physical act of forcibly gaining entry into a locked or barred area.