Binomial Theorem and Its Simple Applications: JEE Main 2025 Mathematics question

Let the coefficients of three consecutive terms $T_r$, $T_{r+1}$ and $T_{r+2}$ in the binomial expansion of $(a+b)^{12}$ be in a G.P. and let $p$ be the number of all possible values of $r$. Let $q$ be the sum of all rational terms in the binomial expansion of $(\sqrt[4]{3}+\sqrt[4]{4})^{12}$. Then $p+q$ is equal to: