How did the sabbatical year and jubilee year fit into ancient Middle Eastern seven-year cycles?

In ancient Hebrew law, the sabbatical year and the jubilee year were structured around the significance of the number seven, which served as a fundamental unit of time in Judaism.512

• Sabbatical Year: Observed every seventh year, this was a period of rest for the land. During this time, agricultural cultivation was omitted, reflecting the principle of the Sabbath as a time for cessation of work and sanctification.341
• Jubilee Year: This occurred every 50th year, following a cycle of seven sabbatical periods ($7\times 7=49$ years). The jubilee year functioned as a time of emancipation and restoration, characterized by the release of enslaved Hebrews, the return of alienated lands to their original owners, and the continued suspension of land cultivation.4

These cycles integrated agricultural practices with religious and social obligations, reinforcing the Jewish religious year as a framework for historical commemoration and social cohesiveness.51