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Wiktionary
press on

vb. (context idiomatic English) to persist, continue to advance

WordNet
press on

v. continue moving forward [syn: push on, plough on]

Wikipedia
Press On

Press On is the Grammy Award-winning second album by singer June Carter Cash. It was released in 1999 by the Risk Records label and then later re-released by the Dualtone label. The album is notable for including Carter Cash performing her composition " Ring of Fire", which is more closely associated with her husband, Johnny Cash.

The album was produced by John Carter Cash (Johnny Cash & June Carter Cash's only son) and J.J. Blair.