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Mathematics

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Triangle ABC has ∠A=40∘, ∠B=60∘, ∠C=80∘. Points M,N trisect the side BC and points P,Q trisect the side AC. The lines AM,AN,BP,BQ intersect at the points S,T,U,V as shown in the figure below, dividing the triangle into 9 regions. Determine the smallest possible value of [ABC]+[STUV] such that both [ABC] and [STUV] are positive integers.

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