Vortex thermal fluctuations in heavily underdoped [Formula presented] ([Formula presented]) are studied using Josephson plasma resonance. From the zero-field data, we obtain the [Formula presented]-axis penetration depth [Formula presented] and the anisotropy ratio [Formula presented]. The low plasma frequency allows us to study phase correlations over the whole vortex solid state and to extract a wandering length [Formula presented] of vortex pancakes. The temperature dependence of [Formula presented] as well as its increase with dc magnetic field is explained by the renormalization of the vortex line tension by the fluctuations, suggesting that this softening is responsible for the dissociation of the vortices at the first order transition. © 2003 The American Physical Society.