An Ambitious Plan

An Ambitious Plan is a main quest $$

Detailed walkthrough
Take the elevator to the top of Fizztop Mountain. Gage will explain the situation: the three raider gangs inside Nuka-World are on the verge of full-scale war as a result of Colter's laziness, and he asks you to meet with the leaders of each gang to prove yourself, and gain their respect and support. A medium speech check gets Gage to inform that the Disciples appreciate violence, the Operators favor money, and the Pack value a show of strength.

Through the door into Fizztop Grille, the new quarters can be examined. Cooking stations, chemistry, power armor stations, and a terminal detailing Colter's slow decline from the feared Overboss into another target for the gangs. Taking the elevator down to the lobby, look on the opposite side of the desk under the leftmost space for a bottle of Nuka-Cola Victory.

Outside the Grille, three markers are now present: Fizztop Mountain (Disciples), The Parlor (Operators), Bradberton Amphitheater (Pack). Go to the three markers, in any order, to meet with the respective gang leaders: Nisha of the Disciples, Mags and William Black of the Operators and Mason of the Pack.
 * Passing a hard Charisma check when talking to Mason during this quest will reward The Problem Solver. It is necessary however to only use right arrow (rude) answers before. While it is okay to use the inquiring answers (up) to get more information, any left or down will lock you out of receiving the weapon. If the Sole Survivor only chooses the right arrow (rude) responses WITHOUT selecting any up arrow dialogue options, the final Charisma check to get the Problem Solver will be medium, rather than hard.

Once all three locations have been visited, return to Gage in the Overboss' quarters. He states that to once again get the operations neglected by Colter going the player character must investigate the five parks, excluding Nuka-Town, that comprise Nuka-World and plant the flag of a gang, declaring that park their territory. Doing so for each gang will help smooth things over, though for every park given to one gang, the others will become jealous. After giving the player character the rundown, Gage offers to accompany them for the duration of the following quests, providing interesting dialogue if accepted.

Bugs
The player character might be unable to start the conversation with Nisha or finish the conversation with Mags Black. To bypass this and continue the quest, use the console command.