  We report on the coordinated observations of the neutron star low-mass X-ray
binary (NS-LMXB) \gx in X-rays (IXPE, NICER, Nustar and INTEGRAL), optical (REM
and LCO), near-infrared (REM), mid-infrared (VLT VISIR), and radio (ATCA). This
Z-source was observed by \IXPE twice in March-April 2023 (Obs. 1 and 2). In the
radio band, the source was detected, but only upper-limits to the linear
polarization were obtained at a $3\sigma$ level of $6.1\%$ at 5.5 GHz and
$5.9\%$ at 9 GHz in Obs.~1 and $12.5\%$ at 5.5~GHz and $20\%$ at 9~GHz in
Obs.~2. The mid-IR, near-IR and optical observations suggest the presence of a
compact jet which peaks in the mid- or far-IR. The X-ray polarization degree
was found to be $3.7\% \pm 0.4 \%$ (at $90\%$ confidence level) during Obs.~1
when the source was in the horizontal branch of the Z-track and $1.8\% \pm 0.4
\%$ during Obs.~2 when the source was in the normal-flaring branch. These
results confirm the variation of polarization degree as a function of the
position of the source in the color-color diagram as for previously observed
Z-track sources (Cyg~X-2 and XTE~1701$-$462). Evidence for a variation of the
polarization angle $\sim 20^\circ$ with energy is found in both observations,
likely related to the different, non-orthogonal polarization angles of the disk
and Comptonization components which peak at different energies.
