You are cast away on an island, it is a paradise and you landed there by accident. No one else is around and you'd like to get off the island. One day a ship arrives to your rescue with passengers aboard, although they've been attacked by pirates claiming to be lost travelers so they don't trust you. They ask for indentification to prove your identity, early on in despair you dropped an item at the bottom of a murky pond while you were trying to access a cave in the rain. This item can prove your identity without a doubt. It's incredibly hard to see under the water and the depth is extremely deep, your item is very small. An almost impossible feat.
What do you do in order to get off the island?
1) Take a deep breath, try to remain calm, swim to the bottom and try to retrieve the item without drowning and repeat as necessary
2) Attempt to craft a fake item to prove your identity from the materials on the island and hope you aren't discovered when you get to port
3) Get used to life on the island and wait for another ship to arrive to your rescue that will believe your story
It's also important to note that talking your way out of this is completely useless, the people on the ship have already had their trust abused and won't listen to a thing you have to say.