I can't be a politician but many people commenting here don't know anything about current affairs.
Can you fight? the answer is no because China will join the war, It is China who always saves it. US cannot invite Pakistan because China won't allow it. If we apply sanctions over Pakistan then Pakistan can do the same, it can interrupt EU-China trade. I think Pakistan may join the EU block if more facilities offered.
Isn't Pakistan in South East Asia
Nope, Pakistan is in South Asia.
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Geographically, how's it possible for a country surrounded by Asian countries be a part of EU? Politically, Pakistan is a China's puppet and China will never allow its dog to follow a US ally like EU.