Learn German: Ich habe daran gedacht.

denken is a "mixed" verb. This means its past participle mixes rules from regular and irregular verbs. Like regular verbs, it starts with ge- and ends with -t. But like irregular verbs, its stem changes—here, from denk- to dach-.

Why do we use habe here if the English translation is just "I thought"?

In spoken German, the Perfekt tense (using a helper verb like habe + a past participle like gedacht) is the most common way to talk about the past. While English uses the simple past ("I thought") very often, German prefers this "have thought" structure for everyday conversations.

Where does the word daran come from?

In German, to "think about" something is denken an (literally "to think at"). When you want to say "think about it", you combine da (there) and an (at/about) to make daran. The extra -r- is added between the two vowels to make it easier to pronounce.

Could I just say "Ich habe an es gedacht" instead of using daran?