# Is it possible to form a PDA for this language?

$$L=\left \{ a^nb^m|n\leq m\leq 2n \right \}$$ Is this even context free?
I am asking because by looking at the condition, for an expression that holds:$$n< m<2n$$ can be written as : $$a^nb^nb^c (c.
Following this term(taken from geeks for geeks https://www.geeksforgeeks.org/check-if-the-language-is-context-free-or-not/) :"An expression that involves counting and comparison of three or more variables independently is not context free language, as stack allows comparison of only two variables at a time."
So here I need to make sure that number of first b's is the same as a's and the second b's are less than n$$(c, which makes me think that L might not be context free(although it specified clearly to build PDA for this).

Hint: The language has the form $$L = \{a^j a^k b^k b^{2j}\}$$. Build a PDA that non-deterministically guesses $$j$$. (I assume you know how to build a PDA for $$\{a^n b^n\}$$ and $$\{a^n b^{2n}\}$$.)