This one will be difficult for most people.
"Another" can be divided into "an other" for analysis. If you would substitute "an" or "a" for "another", use "another".
Normally other is something which is specific and distinct from those before it.
Another is distinct from those before it but is normally is not specific.
For example, if I have two pens and I give you one that doesn't work, you might ask me for the other one. You are specifically asking for THE other pen.
However, if I have 100 pens and I give you one that doesn't work, you would ask me for another. You don't really care which of the 99 other pens that I give you. Note that I use "other" here, because I'm specifically referring to the 99 pens that I have not already given you.
1.Give me some _____ pen.
Substituting "a", we see this doesn't work (Give me some another pen). Use "other" (Give me some other pen).
2. Give me ______ pen.
Substituting "a", we see this does work (Give me a pen). Use "another" (Give me another pen).