Modern Computer Use Agents (CUAs) directly interact with graphical user interfaces and execute third-party web tools, exposing them to indirect prompt injection across every rendered page and tool response. While the Dual-LLM pattern is the primary system-level architecture offering formal security guarantees - using an isolated Planner LLM (P-LLM) to fix execution paths before processing untrusted inputs via a Quarantined LLM (Q-LLM) - these guarantees break down in graphical environments. Because CUA interaction is inherently dynamic, plans cannot remain data-independent; they must branch based on anticipated runtime web content - covering all possible cases the agent may encounter. This exposes agents to branch steering attacks, where an adversary crafts untrusted data to coerce a CUA down a hazardous, pre-approved branch without injecting explicit instructions. We systematically study branch steering attacks and introduce STEER-Bench (101 tasks across 9 domains), showing high attack success against both standard (94.4%) and vanilla Dual-LLM (89.5%) CUAs. We then propose COBRA, an architecture that pairs trusted branching plans with ahead-of-time capability constraints, strictly bounding the parameters and destinations each branch may execute. On STEER-Bench, COBRA reduces attack success to 0% while retaining 97% benign utility.

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