diff --git a/firedrake/assemble.py b/firedrake/assemble.py
index ca5836be95..e495995897 100644
--- a/firedrake/assemble.py
+++ b/firedrake/assemble.py
@@ -503,6 +503,14 @@ def base_form_assembly_visitor(self, expr, tensor, bcs, *args):
                     with lhs.dat.vec_ro as x, rhs.dat.vec_ro as y:
                         res = x.dot(y)
                     return res
+                elif isinstance(rhs, matrix.MatrixBase):
+                    # Compute action(Cofunc, Mat) => Mat^* @ Cofunc
+                    petsc_mat = rhs.petscmat
+                    (_, col) = rhs.arguments()
+                    res = tensor if tensor else firedrake.Function(col.function_space().dual())
+                    with lhs.dat.vec_ro as v_vec, res.dat.vec as res_vec:
+                        petsc_mat.multHermitian(v_vec, res_vec)
+                    return res
                 else:
                     raise TypeError("Incompatible RHS for Action.")
             else:
@@ -830,6 +838,12 @@ def restructure_base_form(expr, visited=None):
                 # Replace arguments
                 return ufl.replace(right, replace_map)
 
+            # Action(Adjoint(A), w*) -> Action(w*, A)
+            if isinstance(left, ufl.Adjoint) and not isinstance(right, firedrake.Function) and is_rank_1(right):
+                # TODO: ufl.action(Coefficient, Form) currently fails. When it is fixed, we can remove the
+                # `not isinstance(right, firedrake.Function)` check.
+                return ufl.action(right, left.form())
+
         # -- Case (4) -- #
         if isinstance(expr, ufl.Adjoint) and isinstance(expr.form(), ufl.core.base_form_operator.BaseFormOperator):
             B = expr.form()
diff --git a/tests/firedrake/regression/test_interp_dual.py b/tests/firedrake/regression/test_interp_dual.py
index 000b1023b2..b0ce971a95 100644
--- a/tests/firedrake/regression/test_interp_dual.py
+++ b/tests/firedrake/regression/test_interp_dual.py
@@ -2,6 +2,7 @@
 import numpy as np
 from firedrake import *
 from firedrake.utils import complex_mode
+from firedrake.matrix import MatrixBase
 import ufl
 
 
@@ -352,3 +353,45 @@ def test_interp_dual_mixed(source_space, target_space):
             assert result is tensor
         for x, y, in zip(result.subfunctions, expected.subfunctions):
             assert np.allclose(x.dat.data_ro, y.dat.data_ro)
+
+
+def test_assemble_action_adjoint(V1, V2):
+    u = TrialFunction(V1)
+
+    a = interpolate(u, V2)  # V1 x V2^* -> R, equiv. V1 -> V2
+    assert a.arguments() == (TestFunction(V2.dual()), TrialFunction(V1))
+
+    f_form = inner(1, TestFunction(V2)) * dx
+
+    for f in (f_form, assemble(f_form)):
+        expr = action(adjoint(assemble(a)), f)
+        assert isinstance(expr, Action)
+        res = assemble(expr)
+        assert isinstance(res, Cofunction)
+        assert res.function_space() == V1.dual()
+
+        expr2 = action(f, a)  # This simplifies into an Interpolate
+        assert isinstance(expr2, Interpolate)
+        res2 = assemble(expr2)
+        assert isinstance(res2, Cofunction)
+        assert res2.function_space() == V1.dual()
+        assert np.allclose(res.dat.data, res2.dat.data)
+
+        A = assemble(a)
+        assert isinstance(A, MatrixBase)
+
+        # This doesn't explicitly assemble the adjoint of A, but uses multHermitian
+        expr3 = action(f, A)
+        assert isinstance(expr3, Action)
+        res3 = assemble(expr3)
+        assert isinstance(res3, Cofunction)
+        assert res3.function_space() == V1.dual()
+        assert np.allclose(res.dat.data, res3.dat.data)
+
+        # This is simplified into action(f, A) to avoid explicit assembly of adjoint(A)
+        expr4 = action(adjoint(A), f)
+        assert isinstance(expr4, Action)
+        res4 = assemble(expr4)
+        assert isinstance(res4, Cofunction)
+        assert res4.function_space() == V1.dual()
+        assert np.allclose(res.dat.data, res4.dat.data)