So you're using the Project Tool to re-projecting a map into a new projection.
Before you can start the process, you have to choose from the many transformations. The attached file (World Projections.xls) lists where in the world each projection transformation should be used.
For example, if your map is in PSAD56, and you want to project it to WGS84, the Project Tool will ask you which transformation you want. Checking the lists for Bolivia, I find: PSAD_1956_To_WGS_1984_2