Now I Know My ABCs

Calculus Level 2

Given that \(\color{green}{a}\), \(\color{red}{b}\) and \(\color{blue}{c}\) are nonnegative real numbers such that \[\Large \color{green}{a}^{\color{red}{b}^{\color{blue}{c}}}=\color{red}{b}^{\color{blue}{c}},\] find the maximum possible value of \(\color{green}{a}\).

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