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Here, we report a new high precision measurement of the proton elastic form factor ratio μpGE/GM for the four-momentum transfer squared Q2 = 0.3-0.7 (GeV/c)2. The measurement was performed at Jefferson Lab (JLab) in Hall A using recoil polarimetry. With the achieved ~1% total uncertainty, the new data clearly show that the deviation of the ratio μpGE/GM from unity observed in previous polarization measurements at high Q2 continues down to the lowest Q2 value of this measurement. The updated global fit that includes the new results yields in this Q2 range an electric (magnetic) form factor ~2% smaller (~1% larger) than the previous global fit. We obtain new extractions of the proton electric and magnetic radii, which are (rE2)1/2 = 0.875 ± 0.010 fm and (rM2)1/2 = 0.867 ± 0.020 fm. Moreover, the charge radius is consistent with other recent extractions based on the electron-proton interaction, including the atomic hydrogen Lamb shift measruements, which suggests a missing correction in the comparison of measurements of the proton charge radius using electron probes and the recent extraction from the muonic hydrogen Lamb shift.