In the coming decade the Gaia satellite will measure the positions and velocities of an unprecedented number of stars in our Galaxy, with unprecedented precision. Among many firsts, this revolutionary new data set will include full six-dimensional phase space information for millions of stars in the Galactic halo, including stars in many tidal streams. These streams, the products of hierarchical accretion, can be used to infer the Galactic gravitational potential thanks to the common origin of the stars in each one. I present a method for doing so by maximizing the information content (i.e. clumpiness) of the action space of the stream stars. This statistical approach eliminates the need to assign stars to particular streams, allowing us to fit the entire accreted stellar halo simultaneously. Using a toy model of the stellar halo in a known potential, and including updated error models for Gaia, I explore the effect on our ability to constrain the Galactic potential of combining Gaia's exquisite proper motion measurements with other information from planned or proposed surveys, such as radial velocities for faint stars, precise distance measurements for RR Lyrae, and/or chemical abundances (which can be added to the fit as extra clustering dimensions). These additional data, among others, will play a crucial role in maximizing our knowledge of the Galactic mass distribution.