  The charged pion multiplicity ratio in intermediate energy heavy-ion
collisions, a probe of the density dependence of symmetry energy above the
saturation point, has been proven in a previous study to be extremely sensitive
to the strength of the isovector $\Delta$(1232) potential in nuclear matter. As
there is no knowledge, either from theory or experiment, about the magnitude of
this quantity, the extraction of constraints on the slope of the symmetry
energy at saturation by using exclusively the mentioned observable is hindered
at present. It is shown that, by including the ratio of average $p_T$ of
charged pions $\langle p_T^{(\pi^+)}\rangle/\langle p_T^{(\pi^-)}\rangle$ in
the list of fitted observables, the noted problem can be circumvented. A
realistic description of this observable requires accounting for the
interaction of pions with the dense nuclear matter environment by the
incorporation of the so called $S$-wave and $P$-wave pion optical potentials.
This is performed within the framework of a quantum molecular dynamics
transport model that enforces the conservation of the total energy of the
system. It is shown that constraints on the slope of the symmetry energy at
saturation density and the strength of the $\Delta$(1232) potential can be
simultaneously extracted. A symmetry energy with a value of the slope parameter
$L>$ 50 MeV is favored, at 1$\sigma$ confidence level, from a comparison with
published FOPI experimental data. A precise constraint will require
experimental data more accurate than presently available, particularly for the
charged pion multiplicity ratio, and better knowledge of the density and
momentum dependence of the pion potential for the whole range of these two
variables probed in intermediate energy heavy-ion collisions.
