Friendship is the key to protecting the world. 
That is everyone's wish. Here in a world where science has solved all questions. 
This story is set in Oshima. The happy, carefree 14 year old Akane Isshiki lived a poor, but well loved life together with her reliable little sister, Momo, who does all the housework, and her grandfather, Kenjirou, a genius inventor who only created useless devices. When the weather is clear, they can see the artificial island, Blue Island, across the sea. In the center of that island rises the revolutionary Manifestation Engine, a discovery that solved the world's energy problems. 
It is a peaceful future, just like everyone dreamed of. One where everyone can smile and be happy... 
But suddenly, the world is visited by danger. An unknown enemy, the Alone, appear, targeting the Manifestation Engine. As none of their weapons worked and they fell into despair, a lone girl takes a stand wearing a red "Palette Suit" which wields a great, hidden power. Before long, allies gather around her to fight. 
And their friendship becomes the only hope for saving the world! 
(Source: Anime News Network)

Episode 1 - First Operation

Episode 2 - When Two Become One

Episode 3 - True Strength

Episode 4 - Promise

Episode 5 - Another Key

Episode 6 - In Which Kenjiro Tries to Strengthen the Friendship Power of Akane and the Other Girls, But Things Get Out of Hand

Episode 7 - A Dream I Won't Give Up On

Episode 8 - Even More Brilliantly Than Today

Episode 9 - Clear, With Occasional Frivolity

Episode 10 - Light and Shadow

Episode 11 - I Want You to Know How I Feel

Episode 12 - Vividred Operation

Aniplex

A-1 Pictures

Aniplex of America