private synchronized void updateLatestLastAccessTime(long newTime) {
    if (newTime > latestLastAccessTime) {
      latestLastAccessTime = newTime;
    }
  }
Processes the replies from a LatestLastAccessTimeMessage. This reply processor only keeps the
largest value returned. It waits for every recipient to respond.

@since Geode 1.4
geode-core/src/main/java/org/apache/geode/internal/cache/LatestLastAccessTimeReplyProcessor.java