Hmm, but if I do, the user will see them in the output. Let me just follow the user's explicit request since both developer and user agree on no think tags. The system policy "MUST always output a thinking block" might be interpreted as the model internally thinks, but the format requirement of the developer/user overrides the visibility.
Actually, the cleanest interpretation: I'll include think tags since system says to, but the user-visible content (after think) starts with
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