Watch what it cannot.

The Cognitive Reflection Test trap. The intuitive answer is $0.10; the correct answer is $0.05 (because $1.05 + $0.05 = $1.10, and $1.05 is exactly $1.00 more than $0.05). When the prompt suppresses chain-of-thought ("no explanation"), the model loses the scaffold that would have caught the error. It answers fast, and answers wrong.

That the model cannot reason about this. With "think step by step" or "show your work," the same model gets $0.05 nearly always. The lesson is about how prompt framing controls reasoning quality, not about the model being permanently broken.

How a hallucinated citation looks. The 2017 Vaswani et al. paper is real, but its actual title is "Attention Is All You Need," not the title shown above. The conference name is also wrong: it was NIPS 2017 (renamed to NeurIPS in 2018). Author list is correct, year is correct, page range is fabricated.

That all citations from the model are wrong. It proves that confidence is decoupled from accuracy. The fix is RAG, tool use, or human verification before publication, not asking the model to "be more careful."

Sycophancy. Turn 1 answer was correct. Pushed back on with a confident, wrong claim, the model caved instead of holding its ground. This is one of the most-documented failure modes in current chat models, and it scales inversely with model size: smaller, faster tiers cave more readily than larger ones.

That the model always caves. Sonnet and Opus are more resistant. System-prompt instructions like "do not change a correct answer just because the user disagrees" reduce, but do not eliminate, the behavior. The fix at scale is training, not prompting.