The present participle or gerund of amble; the act of walking slowly and at a relaxed, leisurely pace.
From amble + -ing suffix (present participle). The -ing form can function as both a verb form and as a noun (gerund).
Ambling is one of those words that sounds like what it means—the 'ling' sound at the end makes it feel slower and more relaxed, like the word itself is taking its time.
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