Nevertheless, simplify-then-guess alone is not enough to mitigate error avalanching. We perform an
additional self-consistency check based on commutativity. Specifically, we ask the model to solve
independently (via simplify-then-guess) both a problem a + b and its twin b + a. If the generated
solutions are not equal, we discard these problems from the dataset. For fast-type addition problems,
this check requires that a problem and its twin have answers that are identical, as measured by an
exact string match. For slow-type addition problems, this commutativity check is slightly more
difficult due to the observation that the chain-of-thought reasoning utterance for A + B is not the
same as the answer for B + A. Instead, SECToR checks that the answers generated by simplifying
for one step, followed by immediately fast adding the subproblem emit identical answers for both a
problem and its commutative twin.

3.5 RESULTS
CHAIN-OF-THOUGHTREASONING IS APOLICY IMPROVEMENTOPERATOR