Computer use agents are evaluated almost exclusively on atomic desktop tasks, but realistic desktop work requires sustaining state across multiple objectives. We study this gap with ChainWorld, which composes atomic OSWorld tasks into long horizon desktop workloads through directional compatibility search while preserving the source evaluators. The resulting workload contains 347 chains of length two to four and compares two renderings of the same task sequence. In single turn evaluation, all tasks are presented together in one prompt. In multi turn evaluation, tasks are revealed one at a time. Across four current computer use agents, maximum chain completion is 31%. Multi turn evaluation improves completion for three models, but both protocols remain challenging. The two protocols also expose different failure profiles. Single turn failures concentrate on artifact precision, while multi turn failures more often reflect session management problems such as fragmented progress and later turn disengagement.

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