  We prove that every acylindrically hyperbolic group that has no non-trivial
finite normal subgroup satisfies a strong ping pong property, the $P_{naive}$
property: for any finite collection of elements $h_1, \dots, h_k$, there exists
another element $\gamma\neq 1$ such that for all $i$, $\langle h_i, \gamma
\rangle = \langle h_i \rangle* \langle \gamma \rangle$. We also obtain that if
a collection of subgroups $H_1, \dots, H_k$ is a hyperbolically embedded
collection, then there is $\gamma \neq 1$ such that for all $i$, $\langle H_i,
\gamma \rangle = H_i * \langle \gamma \rangle$.
