if I'm not mistaken, other is used with a plural noun and another - with a singular one (an+other), e.g. other people - another person

another - любой другой ( один из многих), еще один other - не этот, а тот ( один из двух)

Other - Used to refer to a person or thing that is different or distinct from one already mentioned or known about. Another - Used to refer to an additional person or thing of the same type as one already mentioned or known about; one more; a further.

However, you can use "other" with singular nouns if you're using the word "the". Example: I want the other pickle. You cannot say: I want the another pickle (it's like saying "I want the an egg")

Examples: I want the other pickles. (plural) I want another pickle. (singular)