Moving forward seems to be specific to the original direction of the object being controlled

So I have this code written up to move the player around and have them be able to look around, which works, but if I look to the left, pressing "W" still moves the player in the same direction. How can I adjust this so the player moves in whatever direction the player is facing? Any help is greatly appreciated!

Here is the code I have below:

 public float movementRate = 2.0f;
     public GameObject player;
 
     public float mouseSensitivity = 100.0f;
     public float clampAngle = 80.0f;
 
     private float rotY = 0.0f;
     private float rotX = 0.0f;
 
     void Start()
     {
         Vector3 rot = transform.localRotation.eulerAngles;
         rotY = rot.y;
         rotX = rot.x;
     }
 
     void Update()
     {
         float horizontalInput = Input.GetAxis("Horizontal");
         float verticalInput = Input.GetAxis("Vertical");
 
         player.transform.position += new Vector3(horizontalInput * movementRate * Time.deltaTime, 0, 0);
         player.transform.position += new Vector3(0, 0, verticalInput * movementRate * Time.deltaTime);
 
         float mouseX = Input.GetAxis("Mouse X");
         float mouseY = -Input.GetAxis("Mouse Y");
 
         rotY += mouseX * mouseSensitivity * Time.deltaTime;
         rotX += mouseY * mouseSensitivity * Time.deltaTime;
 
         rotX = Mathf.Clamp(rotX, -clampAngle, clampAngle);
 
         Quaternion localRotation = Quaternion.Euler(rotX, rotY, 0.0f);
         transform.rotation = localRotation;
     }