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ASSIST integrates test particle trajectories in the field of the Sun, Moon, planets, and massive asteroids, with the positions of the masses obtained from the JPL DE441 ephemeris and its associated asteroid perturber file. Using REBOUND's (ascl:1110.016) IAS15 integrator, ASSIST incorporates the most significant gravitational harmonics and general relativistic corrections and accounts for position- and velocity-dependent non-gravitational effects. The first-order variational equations are included for all terms to support orbit fitting and covariance mapping.