Solar flares and coronal mass ejections (CMEs) are closely coupled through magnetic reconnection. CMEs are usually accelerated impulsively within the low solar corona, synchronized with the impulsive flare energy release. We investigate the dynamic evolution of a fast CME and its associated X2.8 flare occurring on 2013 May 13. The CME experiences two distinct phases of enhanced acceleration, an impulsive one with a peak value of ~5 km s$^{-2}$ followed by an extended phase with accelerations up to 0.7 km s$^{-2}$. The two-phase CME dynamics is associated with a two-episode flare energy release. While the first episode is consistent with the standard eruption of a magnetic flux rope, the second episode of flare energy release is initiated by the reconnection of a large-scale loop in the aftermath of the eruption and produces stronger nonthermal emission up to $gamma$-rays. In addition, this long-duration flare reveals clear signs of ongoing magnetic reconnection during the decay phase, evidenced by extended HXR bursts with energies up to 100--300 keV and intermittent downflows of reconnected loops for >4 hours. The observations reveal that the two-step flare reconnection substantially contributes to the two-phase CME acceleration, and the impulsive CME acceleration precedes the most intense flare energy release. The implications of this non-standard flare/CME observation are discussed.
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