= Solution
The <Proca action> is invariant under spacetime translations and proper continuous <Lorentz transformations>, together forming the connected <Poincaré group>. The fixed nonzero <mass> excludes scale invariance. In four dimensions, a dimensionless <action> and the canonical <kinetic term> imply
$$
\boxed{[A^\mu]=1,\qquad[F^{\mu\nu}]=2,\qquad[m_A]=1.}
$$
These are <mass dimensions>. The field-strength term is invariant under $A_\mu\to A_\mu+\partial_\mu\chi$, but the <mass> term is not: its change contains $m_A^2 A^\mu\partial_\mu\chi+\tfrac12m_A^2(\partial\chi)^2$. Thus the displayed massive-vector theory has no Maxwell-type local gauge invariance. The massless limit has a different constraint structure.
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