\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
The following "proof" by equivalence leads to the absurd conclusion that \(1=0\). Identify the incorrect step and explain the error in the reasoning.$$\begin{aligned} && a &= -\frac12 \\ \Leftrightarrow && 2a &= -1 \\ \Leftrightarrow && 2a+1 &= 0 \\ \Leftrightarrow && a^2+2a+1 &= a^2 \\ \Leftrightarrow && (a+1)^2 &= a^2 \\ \Leftrightarrow && a+1 &= a \\ \Leftrightarrow && 1 &= 0\end{aligned}$$
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