Add unique header to multiple lines

I have a file of lines with the following format:
AACCCGTAGATCCGAACTTGTG ACCCGTAGATCCGAACTTGTG CCGTAGATCCGAACTTGTG CGTAGATCCGAACTTGT I want to give a header to each line, using awk, where the header is equal to the line that follows, like this:

     >AACCCGTAGATCCGAACTTGTG     AACCCGTAGATCCGAACTTGTG    >ACCCGTAGATCCGAACTTGTG     ACCCGTAGATCCGAACTTGTG    >CCGTAGATCCGAACTTGTG     CCGTAGATCCGAACTTGTG    >CGTAGATCCGAACTTGT     CGTAGATCCGAACTTGT

I tried this so far:

awk '{ printf("\n"); print">"$0; }'

   >AACCCGTAGATCCGAACTTGTG         >ACCCGTAGATCCGAACTTGTG         >CCGTAGATCCGAACTTGTG         >CGTAGATCCGAACTTGT

awk '{print ">" $0 "\n" $0}' file

Tested the below on GNU sed:

sed 's/.*/>&\n&/' file

Or maybe this one:

awk '{print ""; for (i=1; i<=NF; i++) printf "\t>%s\t%s", $i, $i; printf "\n"}' file

    >AACCCGTAGATCCGAACTTGTG    AACCCGTAGATCCGAACTTGTG    >ACCCGTAGATCCGAACTTGTG    ACCCGTAGATCCGAACTTGTG    >CCGTAGATCCGAACTTGTG    CCGTAGATCCGAACTTGTG    >CGTAGATCCGAACTTGT    CGTAGATCCGAACTTGT