Lord Krishna says: "What is action, what is inaction? Even the wise are herein perplexed. I will declare to thee the action by knowing which thou shalt be freed from evil. It is needful to discriminate unlawful action, to discriminate inaction-the path of action is mysterious. He who seeth inaction in action and action in inaction, he is wise among men, he is harmonious, even while performing all action." Gita: Ch. III-16, 17.
People generally think that action means movement of the body, and inaction means the absence of it, to sit quiet. Sri Sankara writes: "He who sees inaction in action, i.e., he who has the right knowledge that action, which is commonly supposed by all to pertain to the Self, does not really belong to the Self, just as motion does not really pertain to the trees (on the shore of the river) which appear (to a man on board the ship) to move in the opposite direction, and who sees action in inaction, i.e., he who knows that even inaction is action,-for, inaction is but a cessation of bodily and mental activities, and like action it is falsely attributed to the Self and causes the feeling of egoism as expressed in the words "quiet and doing nothing, I sit happy"-he who can realise the nature of action and inaction as now explained is wise among men: "He is a devout Yogin, he is the performer of actions, he is released from evil and has achieved all."
Lord Krishna says: "Having abandoned attachment to the fruit of action, always content, nowhere seeking refuge, he is not doing anything, although doing actions. Hoping for naught, his mind and self controlled, having abandoned all greed, performing action by the body alone he doth not commit sin. Content with whatsoever he obtaineth without effort, free from the pairs of opposites, without envy, balanced in success and failure, though acting he is not bound. Of one with attachment dead, harmonious and with his thoughts controlled in wisdom, his works being all sacrifices, all actions melt away. The Eternal the oblation, the Eternal the clarified butter, are offered in the Eternal fire by the Eternal; unto the Eternal verily shall he go, who, in his action, meditateth wholly upon the Eternal. He who hath renounced action by Yoga, who hath rent asunder doubts by wisdom, who is ruled by the Self, actions do not bind, O Arjuna!" Gita: Ch. IV-20 to 24, 41.
When a man regards the action as if it were for him, he has 'action-mentality', and when he treats of it as God-ordained and for God, he being just a spectator, he has 'inaction-mentality'.
If an action is done with Nishkamya Bhava as Isvararpana, then it is no action at all. It is 'inaction in action'.
If you identity yourself with Brahman and stand as a witness of the activities of Prakriti and its effects, mind, Indriyas and body, you will realise 'inaction in action'. Brahman is Nishkriya, Akarta, Niravayava. But he is the primum mobile. He gives a push and Prakriti moves and acts.
He gazes and Prakriti moves and acts. Without His presence Prakriti cannot do anything. Therefore it is Brahman only who really does all actions. This is 'action in inaction' as taught in the Gita.