Hi, Crying Wolf.
Hmmm . . .
To begin, no native speakers – that is, speakers of any language – get tongue-tied. One of the many miracles of language is the ability of speakers to pump out
a breathtaking number of syllables in a given period. Moreover, speech is an unbroken stream of sound. We just tend to think (and there are some old-fashioned (political) views of language hiding behind this notion) that. we. pronounce. each. word. separately.
Thankfully, there exists a system of symbols that allows linguists (which is what I want to be when I grow up) to represent the sounds of (written and spoken) language – and this system, and the field of linguistics in which it is used, is splendidly complicated.
Here's a simple example, on our way to answering your question: the word 'nut' rhymes with 'hut' and 'cut'; and the phonetic representation of 'nut' is [n^t]. Conversely, the word 'put' -- which any sane person might expect to rhyme with 'nut' -- doesn't rhyme with 'nut.' It rhymes with 'soot' and 'foot.' Its phonetic representation is 'put' – in the system, the 'oo'-sound in 'foot' is represented by the symbol [u].
O.k. . . . Now let's tackle '. . . and another thing . . . ' The 'ther' in 'mother' is the 'th'-sound-that-includes-the-'zzzzzz'-in-your-throat (the 'th' in 'mother' not the 'th' in 'path'); and its symbol is [ð]. Next comes the 'er'-sound symbol. Say the word 'sofa' out loud a few times. The 'a' sound is not 'a' as in 'pat' or 'a' as in 'croissant,' is it? No, it is a creature called 'schwa'; and its symbol is [Ə]. Schwas are very very common in language. They are a 'reduced vowel,' which means that they are a sort of 'squashed' sound that we shove into the gaps between consonants as we are pumpin' out those syllables. (Sit down with any English-language text. Read it aloud. Pronounce every 'er' – like the 'er' in 'another' – so that it rhymes with 'her.' Never happen!! You immediately find yourself speeding up, squashing those 'er' sounds into schwas.)
Right, that's enough symbols. Your ' . . . and another thing . . . ' is starting to look like this: [air-ner-nar-ð-Ə-ð-ing]. Note that the 'd' in 'and' got dumped somewhere along the way. Note that thethreewords have become one (unbroken) sound.
In closing, Crying Wolf, I note that, as the English of your question denotes an advanced competence on your part, you might benefit from tangling with the International Phonetic Alphabet. Don't kid yourself. It would be hard, hard work. However, it would put your English on a plane of fluency that is achieved by very very very very few ESL students. Good luck.
Mark in Rocky Gully (was Mark in Perth)