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Fury is a status effect in Mario & Luigi: Bowser's Inside Story and Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey that can only be obtained by Bowser when he takes too much damage during battles.
While under the effects of the Fury status, Bowser flashes red, clenches his fists, and shows a much angrier facial expression with gritted fangs and puffs of smoke spewing overhead. In this state, the damage Bowser deals and takes is doubled, identical to a combination of both POW-Up and DEF-Down. To cure this effect, Bowser can eat a Refreshing Herb, have a set amount of turns pass, or defeat all of the enemies on screen. It is similar to the Great Force from Mario & Luigi: Superstar Saga and Mario & Luigi: Superstar Saga + Bowser's Minions, which doubles the damage the brother who is equipped with it deals and takes.
In the remake, Bowser also goes into this status effect when he reaches low health during the fight with him in Toadley Clinic, and as soon as he does he will fully heal himself with a Drumstick (Bowser X does this too when fought in the Gauntlet).
In Mario & Luigi: Paper Jam, Mario & Luigi: Superstar Saga + Bowser's Minions and Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey, most of the bosses, along with Birdo in Mario & Luigi: Superstar Saga (once Popple is defeated before her) and Princess Shroob in Mario & Luigi: Partners in Time, automatically get this status whenever their health is low enough. For the rest of the battle, they have more attacks, their POW and SPEED increase (alongside DEF in Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey), and some bosses will perform multiple attacks in a single turn. Regular enemies, such as Choombas, go through a similar phase when fired up by Coalbits, making them deal more damage, move faster, and glow red.