<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 A robot is located in one of the cells of an infinite grid paper and can be given the following commands:
- move up (the robot moves to the adjacent cell above);
- move down (the robot moves to the adjacent cell below);
- move left (the robot moves to the adjacent cell to the left);
- move right (the robot moves to the adjacent cell to the right).

For example, if the robot executes a sequence of four commands (up, right, down, left), it will obviously return to its initial position, which means it will be in the same cell from which it started moving. How many different sequences of 8 commands return the robot to its initial position? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
4900
A robot is located in one of the cells of an infinite grid paper and can be given the following commands:
- move up (the robot moves to the adjacent cell above);
- move down (the robot moves to the adjacent cell below);
- move left (the robot moves to the adjacent cell to the left);
- move right (the robot moves to the adjacent cell to the right).

For example, if the robot executes a sequence of four commands (up, right, down, left), it will obviously return to its initial position, which means it will be in the same cell from which it started moving. How many different sequences of 8 commands return the robot to its initial position?
test