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How impulsive solar energetic particle (SEP) events are produced by magnetic-reconnection-driven processes during solar flares remains an outstanding question. Here we report a short-duration SEP event associated with an X-class eruptive flare on 2021 July 3, using a combination of remote sensing observations and in situ measurements. The in situ SEPs were recorded by multiple spacecraft including the Parker Solar Probe. The hard X-ray (HXR) light curve exhibits two impulsive periods. The first period is characterized by a single peak with a rapid rise and decay, while the second period features a more gradual HXR light curve with a harder spectrum. Such observation is consistent with in situ measurements: the energetic electrons were first released during the early impulsive phase when the eruption was initiated. The more energetic in situ electrons were released several minutes later during the second period of the impulsive phase when the eruption was well underway. This second period of energetic electron acceleration also coincides with the release of in situ energetic protons and the onset of an interplanetary type III radio burst. We conclude that these multimessenger observations favor a two-phase particle acceleration scenario: the first, less energetic electron population was produced during the initial reconnection that triggers the flare eruption, and the second, more energetic electron population was accelerated in the region above the loop-top below a well-developed, large-scale reconnection current sheet induced by the eruption.