Xiao Li is a farm owner who grows A, B, and C. He can exchange these crops for agricultural products X and Y. He has discovered the following methods to increase the farm's yield:

Method 1: 2 units of crop A and 1 unit of crop B and 1 unit of crop C can be exchanged for 3 units of product X, and this can be done only once per cycle.

Method 2: 1 unit of crop A and 1 unit of crop B can be exchanged for 2 units of product C, and this can be done only once per cycle.

Method 3: 2 units of crop C and 1 unit of product X can be exchanged for 1 unit of product Y, and this can be done only once per cycle.

Method 4: 1 unit of crop A and 2 units of product X can be exchanged for 1 unit of product Y, and this can be done only once per cycle.

Xiao Li continuously cycles through these methods in the given order, executing one method at a time. After Method 4, start again from Method 1. Continue this cycle until no method can be executed.

Initially there are 8 units of crop A, 3 units of crop B, 7 units of crop C.

First output the entire reasoning process step by step, showing each synthesis step's result. Then wrap your final answer in <<<>>> format as a list showing [remaining_A, remaining_B, remaining_C, obtained_X, obtained_Y]. For example, if there are 1 unit of crop A, 0 units of crop B, 2 units of crop C, and 3 units of product X, 1 unit of product Y remaining, output: <<<[1, 0, 2, 3, 1]>>>