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Button operation that indicates start and finish of simulation


In a notebook with many dynamic modules I have a long simulation which I start with a button.  I would like to give an indication that the simulation is starting and also when it is finished. Below, in a toy example,  I attempt to use a simple message and also an EvaluationMonitor. Both only give results when the simulation is finished. What don't I understand and how do I fix this? Many thanks.

ClearAll[LongSimulation]
LongSimulation[] :=
 TimeConstrained[NDSolve[{Derivative[2][x][t] + x[t] == 0,
         x[0] == 1, Derivative[1][x][0] == 0}, x, {t, 0, 100000*Pi},
       MaxSteps -> Infinity, Method -> {"Projection", "Invariants" ->
             {x[t]^2 + Derivative[1][x][t]^2}},
   EvaluationMonitor :> k++], 3]

k=0;

DynamicModule[{message = " "},
   Column[{Button["Start Simulation", message = "Starting Simulation";
          LongSimulation[]; message = "Simulation Finished"],
   Dynamic[message],
       Dynamic[k]}]]



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