1Why Thinking Longer HelpsExtra time helps when it is used to search, check, and revise; it fails when it only repeats the same mistake more confidently.Frontier 2Search, Verifiers & Budget-ForcingHow better answers emerge when systems explore options, check their work, and spend effort where it matters most.Frontier 3Reasoning vs Latency & CostBetter answers often require more computation, so the practical question is when deeper reasoning is worth the wait and the bill.Frontier 4Reasoning Failure ModesReasoning fails in predictable ways when inputs are weak, assumptions stay hidden, or confidence outruns evidence.Frontier