```python
def gen_plan(state: DrawState):
    
    def calculate_star_points(center, size):
        """
        Calculate the 10 points of a five-pointed star centered at `center` with a given `size`.
        The points are returned in the order they should be connected to draw the star.
        """
        import math

        # Constants
        degrees_per_point = 360 / 5
        radians_per_point = math.radians(degrees_per_point)
        inner_angle = math.radians(36)  # Inner angle between points and center
        outer_radius = size / 2
        inner_radius = outer_radius * math.sin(inner_angle) / math.sin(math.radians(126))

        # Calculate points
        points = []
        for i in range(5):
            outer_x = center[0] + math.cos(i * 2 * radians_per_point) * outer_radius
            outer_y = center[1] + math.sin(i * 2 * radians_per_point) * outer_radius
            inner_x = center[0] + math.cos(i * 2 * radians_per_point + radians_per_point) * inner_radius
            inner_y = center[1] + math.sin(i * 2 * radians_per_point + radians_per_point) * inner_radius
            points.append([outer_x, outer_y])
            points.append([inner_x, inner_y])

        return points

    def create_star_actions(center, size):
        """
        Create the actions to draw a five-pointed star centered at `center` with a given `size`.
        """
        star_points = calculate_star_points(center, size)
        actions = []
        for i in range(len(star_points)):
            x0, y0 = star_points[i]
            x1, y1 = star_points[(i + 1) % len(star_points)]  # Wrap around to close the star
            actions.append(Action("draw_line", [x0, y0, x1, y1]))
        return actions

    # Star parameters
    center = [0.5, 0.35]  # Center of the drawing board (cm)
    size = 0.2            # Size of the star (cm)

    # Generate and return the plan
    return create_star_actions(center, size)
```