  Magnetized turbulence and magnetic reconnection are often invoked to explain
the nonthermal emission observed from a wide variety of astrophysical sources.
By means of fully-kinetic 2D and 3D PIC simulations, we investigate the
interplay between turbulence and reconnection in generating nonthermal
particles in magnetically-dominated pair plasmas. A generic by-product of the
turbulence evolution is the generation of a nonthermal particle spectrum with a
power-law energy range. The power-law slope $p$ is harder for larger
magnetizations and stronger turbulence fluctuations, and it can be as hard as
$p < 2$. The Larmor radius of particles at the high-energy cutoff is comparable
to the size $l$ of the largest eddies. Plasmoid-mediated reconnection, which
self-consistently occurs in the turbulent plasma, controls the physics of
particle injection. Then, particles are further accelerated by stochastic
scattering off turbulent fluctuations. The work done by parallel electric
fields - naturally expected in reconnection layers - is responsible for most of
the initial energy increase, and is proportional to the magnetization $\sigma$
of the system, while the subsequent energy gain, which dominates the overall
energization of high-energy particles, is powered by the perpendicular electric
fields of turbulent fluctuations. The two-stage acceleration process leaves an
imprint in the particle pitch-angle distribution: low-energy particles are
aligned with the field, while the highest energy particles move preferentially
orthogonal to it. The energy diffusion coefficient of stochastic acceleration
scales as $D_\gamma\sim 0.1\sigma(c/l)\gamma^2$, where $\gamma$ is the particle
Lorentz factor. This results in fast acceleration timescales $t_{acc}\sim
(3/\sigma)\,l/c$. Our findings have important implications for understanding
the generation of nonthermal particles in high-energy astrophysical sources.
