He carries on his father's legacy and continues to strive.
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秉承 is formal and literary. In everyday speech, people say 继承 (inherit) or 遵循 (follow). 秉承 appears in official statements, company mission statements, and formal writing.
usage
The object of 秉承 is always something abstract and positive: traditions (传统), principles (原则), beliefs (信念), or a predecessor's wishes (遗志).