def METHOD_NAME(self, state: _odesolver_state.ODESolverState, dt: FloatLike):
    """Perturb the original stopping point.
    Perform one perturbed step and project the solution back to the original
    stopping point.
    Parameters
    ----------
    state
        Current state of the ODE solver.
    dt
        Step-size.
    Returns
    -------
    _odesolver_state.ODESolverState
        New state.
    """
    noisy_step = self.perturb_step(self.rng, dt)
    new_state = self.solver.METHOD_NAME(state, noisy_step)
    scale = noisy_step / dt
    self.scales.append(scale)
    t_new = state.t + dt
    state = _odesolver_state.ODESolverState(
        ivp=state.ivp,
        rv=new_state.rv,
        t=t_new,
        error_estimate=new_state.error_estimate,
        reference_state=new_state.reference_state,
    )
    return state