CFG/PDA Question - (Context Free Grammar) - I need to create a grammar for the Language L = {aⁿb^{n +m}c^m, n 0, m 1 }

I tried something like

S -> aC | bD

C -> aC|bD

D -> bD | cE

E -> cE | c

This works for the correct number of variables i.e. abbbcc, but also works for the incorrect number of variables. i.e. aabbbcc when it should not. How do I design the grammar to only produce the correct strings?

Also, I need to construct a PDA for this same scenario. (we use JFLAP, but any diagram explaining would help me)