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Context.One of the most important open questions in planet formation is how dust grains in a protoplanetary disk manage to overcome growth barriers and form the ∼100 km planet building blocks that we call planetesimals. There appears to be a gap between the largest grains that can be produce by coagulation, and the smallest grains that are needed for the streaming instability (SI) to form planetesimals. Aims.Here we explore the novel hypothesis that dust coagulation and the SI work in tandem; in other words, they form a feedback loop where each one boosts the action of the other to bridge the gap between dust grains and planetesimals. Methods.We developed a semi-analytical model of dust concentration due to the SI, and an analytic model of how the SI affects the fragmentation and radial drift barriers. We then combined them to model our proposed feedback loop. Results.In the fragmentation-limited regime, we find a powerful synergy between the SI and dust growth that drastically increases both grain sizes and densities. We find that a midplane dust-to-gas ratio ofϵ ≥ 0.3 is a sufficient condition for the feedback loop to reach the planetesimal-forming region for turbulence values 10⁻⁴ ≤ α ≤ 10⁻³and grain sizes 0.01 ≤ St ≤ 0.1. In contrast, the drift-limited regime only shows grain growth without significant dust accumulation. In other words, planetesimal formation remains challenging in the drift-dominated regime and dust traps may be required to allow planet formation at wide orbital distances.