Change

open ACCESS, ">> $log" || die "Cannot open $log: $!";
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to be

open ACCESS, ">> $log" or die "Cannot open $log: $!";
#or
open (ACCESS, ">> $log") || die "Cannot open $log: $!";
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Reason: || has higher precedence than , causing

open ACCESS, ">> $log" || die "Cannot open $log: $!";
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to be equivalent to

open ACCESS, ( ">> $log" || die "Cannot open $log: $!"; )
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thus, no error message.