Difficult# What is the Median of Set T?

GMAT-XLVKB9

Set S consists of positive, consecutive integers $a$, $b$, and $c$ where $a < b < c$.

Set T consists of positive, consecutive integers $e$, $f$, and $g$ where $e < f < g$.

The median of Set S is $\cfrac{2}{3} f$.

The median of Set T is $a+7$.

What is the median of Set T?