  In 2002, Fukaya proposed a remarkable explanation of mirror symmetry
detailing the SYZ conjecture by introducing two correspondences: one between
the theory of pseudo-holomorphic curves on a Calabi-Yau manifold $\check{X}$
and the multi-valued Morse theory on the base $\check{B}$ of an SYZ fibration
$\check{p}: \check{X}\to \check{B}$, and the other between deformation theory
of the mirror $X$ and the same multi-valued Morse theory on $\check{B}$. In
this paper, we prove a reformulation of the main conjecture in Fukaya's second
correspondence, where multi-valued Morse theory on the base $\check{B}$ is
replaced by tropical geometry on the Legendre dual $B$. In the proof, we apply
techniques of asymptotic analysis developed in our previous works to
tropicalize the pre-dgBV algebra which governs smoothing of a maximally
degenerate Calabi-Yau log variety introduced in another of our recent work.
Then a comparison between this tropicalized algebra with the dgBV algebra
associated to the deformation theory of the semi-flat part $X_{\text{sf}}
\subseteq X$ allows us to extract consistent scattering diagrams from
appropriate Maurer-Cartan solutions.
