What is the precedence between performing a current congregational prayer and maintaining sequence for missed prayers when time is scarce?

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When a congregational prayer is due and one has missed prayers, sequence is generally waived in favor of the current prayer. Imam Ahmad stated that if one catches the Dhuhr congregation while still needing to complete prior prayers, one should join the Imam for Dhuhr, counting it as one of the missed prayers, and then perform the actual Dhuhr prayer at the end of its time. Regarding an individual fearing missing the congregation for the current prayer while having a missed prayer, one narration suggests sequence is dropped because both the sequence and the congregation are obligatory, forcing a choice, making the person free to choose. The stronger position is that the current prayer is performed with the congregation without needing repetition afterward, especially if time is too limited to make up all missed prayers before the current time expires.