This is a difficult problem for language models, so In order to maintain coherence I will use a detailed long addition strategy(This is unlikely to work at high temperature).

1. Problem setup

    123.0000
    000.2321

2. Single digit additions

    For each column, the digit on top goes in on the left, and the digit on the bottom goes on the right in the parentheses.

    (1+0),(2+0),(3+0),(0+2),(0+3),(0+2),(0+1)

    Next, we add the numbers in each pair of parentheses together, this should be manageable for a language model.
    
    1,2,3,2,3,2,1

3. Carryovers
    
    If we have sums larger than 10, we will need increase the digit to the left by 1. In this case, there are no carryovers, so we can immediately proceed to the final result.

    0,0,0,0,0,0,0

4. Final result

    Since all carryovers are zero, we are done
    1232321 is our sequence of digits. The decimal goes the same number of places from the right as in the original setup, giving us

    123.2321
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