Global symbol "$useragent" requires explicit package name at xxxxx.pl line 8.

This is what I am getting when I execute your code.

The WWW::Mechanize documentation says that click_button works on the "current Form", which might be the source of your problem. please check whether the button is in any form? if it is means try add below example code before click_button() and try.

    # select the first form and examine its contents
    $m->form_number(1);
    my $f = $m->current_form or die "Couldn't get first form!\n";
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