KZ-MO 2021 Problem 1

Given $a,b,c>0$ such that $a+b+c+\frac{1}{abc}=\frac{19}{2}$ What is the greatest value for $a$ ?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.