Sleeping while LO sleeps saved my life for the first few months! Yes, there may be a lot of things to do but some can probably wait and aren't as urgent as you think - if you don't have enough rest, you won't be able to look after LO and might affect your milk supply if you're breastfeeding.
However, I believe that no matter how old your child is - you should just let LO sleep and eat on demand :)
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