Viele Risse haben ausgebessert und geglättet werden müssen.

Questions & Answers about Viele Risse haben ausgebessert und geglättet werden müssen.

Why does this sentence use 'haben ... werden müssen' instead of a past participle like 'gemusst'?
This is the perfect tense of a passive sentence with a modal verb. When a modal verb is used with another verb in the perfect tense, it triggers the 'double infinitive' rule. Instead of using its past participle (gemusst), it stays in the infinitive form (müssen). The passive auxiliary verb also stays in the infinitive (werden instead of worden).
I thought the perfect tense of the passive voice uses 'sein'. Why is 'haben' used here as the conjugated verb?
You are right that a normal passive sentence uses sein for the perfect tense (for example, Viele Risse sind ausgebessert worden). However, when you add a modal verb like müssen to a passive sentence, the auxiliary verb for the perfect tense always switches from sein to haben.
How are two different actions ('ausgebessert' and 'geglättet') handled in this complex verb structure?
Because both main verbs describe actions done to the subject and share the exact same passive and modal helping verbs, you do not need to repeat the grammar. You simply connect their past participles with und (ausgebessert und geglättet) and place the shared helper verbs (werden müssen) just once at the very end of the sentence.
What is the exact word order rule for that cluster of verbs at the end?
In a regular main clause, the conjugated helping verb (haben) takes position two. All the other verbs stack up at the very end in a strict order: first the past participles of the main verbs (ausgebessert und geglättet), followed by the passive helper (werden), and ending with the modal verb (müssen).

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