Can you still use your bonus action and/or reaction when under the effect of a berserker weapon?

When attuned to a Berserker Weapon, if you receive damage and then fail a DC 15 Wisdom saving throw, you go berserk and must use your action to attack the nearest creatures (friend or foe), moving to the next creatures once the nearest ones are defeated. This therefore locks your action and movement.

But what about your bonus action and reaction? Let’s say, for example, that I’m a Level 7 Redemption Paladin in berserk mode but with an Aura of Vitality, could I use my bonus action to heal my ally after the first hit, then use my reaction to take the damage instead of him (Level 7 Redemption Aura) on the second hit ?