Do loop and print result if found, else do loop again: how to get rid of multiple nesting if's in Python

I have a dictionary with thousands of elements of the following structure:

    full_dict={'A': ['B','C','D','E'],
     'B':['A','C','D','E','F','X']
     'X':['W','Y','Z','S'],
     'S':['W','K','T'],
    ...}

where every letter is a word. Every word can be both a key and a value (together with other words) for another dict element.

I am trying to find a "path" from one word to another. For example a path from 'A' to 'S' is A-B-X-S as S is among values of X, X in B and B in A.

Currently, I am using this code:

    query=['A','S']
    if 'S' in full_dict['A']:
        print ('Found during 1st iteration')
    else:
        for i in full_dict['A']:
            if 'S' in full_dict[i]:
                print ('Found during 2nd iteration')
            else:
                for ii in full_dict[i]:
                etc.

I do 10 iterations and it works fine but I wonder if there is a better way to do it. Thank you in advance.