You can use "another" before a noun whenever you can use "a (n)" before a noun. The rules are the same. Another = an other!

When we use ‘ an ’ before ‘ other ’, we write it as one word: another. Another expresses quantity. It means 'additional' or 'one more'. We use another with singular nouns: another chair, another day.

“Other” acts as an adjective or a determiner for plural and noncount nouns, representing general, additional, or distinct items. Conversely, “another” works exclusively with singular nouns. Unlike “other,” “another” does not refer to anything specific and implies one more item or an alternative of the same kind.

The biggest difference between these two words is that “another” is always singular and does not describe anything specific. “Other” is used for plural and noncount nouns that are general. We only use “the other” to refer to specific nouns.

The primary difference between another and other is that both another and other are determiners, but another precedes singular countable nouns or pronouns. Conversely, other precedes a plural countable as well as uncountable nouns and pronouns.