purposelessly

/ˈpɜrpəsləsli/
adverb
  1. In a way that has no aim, goal, or reason.
    • He wandered purposelessly through the mall, not looking for anything in particular.
    • She stared purposelessly out the window, lost in thought.
    • The children ran purposelessly around the playground, laughing without any game in mind.
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