[ParadaCarleton]

With verbose = true, solve(prob, Newton(), options) prints "Newton algorithm failed to converge" only when residuals[end] > tol (src/Newton.jl:113). A NaN residual makes that comparison false, so a Newton run that ends on a NaN residual returns converged = false without the message; the same holds for a final residual equal to tol. The returned flag is already right, because line 114 tests residuals[end] < tol. This PR writes the message condition as the negation of that test, !(residuals[end] < tol), so the message appears whenever the flag says the run failed. A new test in test/newton/test_newton.jl checks that a residual function returning NaN logs the error and returns converged = false.

https://claude.ai/code/session_015sE9Latuiqsp6zSHQ1cshz