Fibonacci Puzzle Game

The "Fibonacci Puzzle Game" is a game similar to the cult puzzle 2048. The player has access to a playing field, 4x4 cells in size. At the beginning of the game, two blocks appear in random cells, which are equal to the number 1. In this puzzle, the player can move the blocks and put them together. Now some rules:
1) You can move the block to any available adjacent cell.
2) After a successful move, two new blocks appear on the field in random free cells.
3) The probability that the new block will be equal to 1 is about 80%, otherwise the block will be equal to 3.
4) To add a block to a neighbor, the sum of their values ​​must equal the next number from the Fibonacci range. For example: 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5. We cannot add 3 and 1 because 4 is not a Fibonacci number.
5) If the player stacked blocks, no new numbers will appear in this step.
6) The game is considered lost if the entire field is filled and not a single block can be added.