The action of a relativistic point particle is its negative rest energy along its worldline, the parameter being its own proper time. $$ S = - mc^2 \int d\tau $$ (see Wikipedia)
Action is energy multiplied with time. How can I imagine the "action" of an unaccelerated point particle which does not seem to deploy any kind of energy?
Further explanation: An oven may emit a certain number of Jsec in a given time, but not an unaccelerated point particle.