ax-engine

Create a Python-based interactive narrative game using the 'ax-engine' package. This game will allow players to explore a mysterious island filled with puzzles and secrets. The player's decisions throughout the game will affect the storyline, leading to multiple endings based on their choices.

The game should have the following features:
1. A main menu where players can start a new game, load a saved game, or exit the game.
2. An interactive map of the island with different locations such as a forest, beach, ruins, and caves.
3. Each location should contain at least one puzzle or challenge for the player to solve.
4. The game should keep track of the player's progress and save it after each session.
5. Players should be able to make choices that influence the story and the environment around them.
6. Include a system to display hints when the player is stuck on a puzzle.
7. Implement a scoring system based on the player's efficiency and success rate in solving puzzles.
8. Offer multiple endings based on the player's choices and performance.

Utilize the 'ax-engine' package to handle the game's logic, user interface, and interaction flow. Specifically, use its capabilities to create dynamic, responsive game elements and to manage the game state efficiently. The package should also help in generating interactive dialogues between characters and handling complex game scenarios seamlessly.