The variety of star formation histories (SFHs) of π§ 6 galaxies provides important insights into early star formation, but has been difficult to systematically quantify. Some observations suggest that many π§ βΌ 6 β 9 galaxies are dominated by old ( 200 Myr) stellar populations, implying significant star formation at π§ 9, while others find that most reionization era galaxies are young ( 10 Myr), consistent with little π§ 9 star formation. In this work, we quantify the distribution of ages and SFHs of UV-bright (β22.5 π β21) galaxies colour-selected to lie at π§ 6.6 β 6.9, a redshift range where stellar and nebular emission can be photometrically separated and galaxy properties robustly inferred, providing the ideal opportunity to systematically study the SFHs of reionization era galaxies. We infer the properties of the sample with two spectral energy distribution (SED) modelling codes and compare their results, finding that stellar masses are largely insensitive to the physical model, but the inferred ages can vary by an order of magnitude. We then infer a distribution of ages assuming a simple, parametric SFH model, finding a median age of βΌ 30 β 100 Myr depending on the SED model. We quantify the fractions of young (β€ 10 Myr) and old (β₯ 250 Myr) galaxies and find that these systems comprise βΌ 10 β 30 per cent and βΌ 20 β 30 per cent of the population, respectively. With a more flexible SFH model, the general shape of the SFHs are consistent with those implied by the simple model (e.g. young galaxies have rapidly rising SFHs). However, stellar masses can differ significantly, with those of young systems sometimes being more than an order of magnitude larger with the flexible SFH. Finally, we quantify the implications of these results for π§ 9 stellar mass assembly and discuss improvements expected from the James Webb Space Telescope.