```python
def gen_plan(state: DrawState, x0: float, y0: float, x1: float, y1: float, x2: float, y2: float, x3: float, y3: float, x4: float, y4: float, x5: float, y5: float, x6: float, y6: float, x7: float, y7: float, x8: float, y8: float, x9: float, y9: float):
    
    
    # Build the bridge
    actions = []

    actions.append(Action("draw_line", [x0, y0, x1, y1]))
    actions.append(Action("draw_line", [x1, y1, x2, y2]))
    actions.append(Action("draw_line", [x2, y2, x3, y3]))
    actions.append(Action("draw_line", [x3, y3, x4, y4]))
    actions.append(Action("draw_line", [x4, y4, x5, y5]))
    actions.append(Action("draw_line", [x5, y5, x6, y6]))
    actions.append(Action("draw_line", [x6, y6, x7, y7]))
    actions.append(Action("draw_line", [x7, y7, x8, y8]))
    actions.append(Action("draw_line", [x8, y8, x9, y9]))
    actions.append(Action("draw_line", [x9, y9, x0, y0]))
    return actions

def gen_initial_guess(initial: DrawState):

    # Initial guess for the five-pointed star vertices
    return {
        "x0": 0.5, "y0": 0.65,
        "x1": 0.6, "y1": 0.5,
        "x2": 0.7, "y2": 0.65,
        "x3": 0.4, "y3": 0.5,
        "x4": 0.5, "y4": 0.35,
        "x5": 0.5, "y5": 0.6,
        "x6": 0.55, "y6": 0.5,
        "x7": 0.6, "y7": 0.6,
        "x8": 0.45, "y8": 0.5,
        "x9": 0.5, "y9": 0.4
    }
```