I know this is late, but could you provide any more context from the text?
You bring up the adverb consciously; deliberately is effectively a synonym of that - so "act deliberately" would be saying the same thing.
But either of these is often used very basically as "on purpose", to clarify that something was not an accident, that "I meant/chose/decided to do that."
And there is less overlap in different forms of the same concepts - e.g. there is not a synonym for deliberation that contains conscious.
The overlap that is the source of the synonymous adverbs is between the adjectives deliberate and conscious.
deliberation, however, is derived from the verb deliberate, whereas there is no verb form of conscious.
I concur with Yulia's comment, that the passage you quoted appears to refer to the 'care' and/or 'thoughtfulness' aspects of deliberation:
Thoughtfulness in decision or action.
thoughtful, careful, or lengthy consideration
But I don't think the advice being given in the passage is merely an elaboration of the definition of deliberation; rather it's recommending how you follow through in your various deliberate actions. In a way it's a suggestion to saturate every detail of your behavior and/or relationships with deliberation.
In this respect, consciously would be appropriate, but (as noted above with regard to deliberately) it would be less vague to use conscientiously:
conscientious: Thorough and assiduous . . . careful and hard-working