The sides of triangles $ABC$ and $ACD$ satisfy the following conditions: $AB = AD = 3$ cm, $BC = 7$ cm, $DC = 11$ cm. What values can the side length $AC$ take if it is an integer number of centimeters, is the average in $\Delta ACD$ and the largest in $\Delta ABC$?

Let's think step by step and output the final answer within \boxed{}.
user