Anne wants to sell her commercial office space in Dubbo. Kate, (Anne's cousin) is an insurance broker and is looking for office space. They meet at a BBQ on 22 February 2022, and they discuss the property. That night Anne sends an email to Kate. The email says:

Further to our discussion I'm happy to sell you the office in Dubbo for $750,000. This is cheaper than the going rate but if I don't have to deal with an estate agent and we can get it all signed off in the next two weeks, it's worth it. I'll get my lawyer to draw up the contract and send it to you.

Kate replies 'Sounds great, I look forward to getting the contract'.

Anne instructs her lawyer to prepare the contract for sale. This incurs various costs for searches and professional fees. The contract is sent to Kate. Shortly after Bill offers Anne $900 000 for the office. Anne contacts Kate and says 'I've been offered more but we had an agreement. If you still want to go ahead, I'll honour that agreement and tell them "It's sold"'.

Kate replies - 'Yes please do that, I'm so grateful, yes I want to buy it I simply haven't been able to get in to see my lawyer'.In fact, Kate has not tried to make an appointment to see her lawyer but has been looking at other cheaper offices.

Three weeks later Anne contacts Kate as she's heard nothing further. Kate replies "I've changed my mind, I'm going to buy somewhere else, unless you want to reduce your price to $500 000". Anne goes back to Bill who says he's found somewhere else so is no longer interested.

1. Does a valid contract exist between Anne and Kate?
2. Assuming there is no valid contract, does Anne have any remedy against Kate?

Your answer must be supported by relevant case law.