```python
def gen_plan(state: DrawState, pos: list, size: float, offsets: list):
    x, y = pos

    # Define the positions for the hash symbol (#) based on the size
    lines = [
        # Vertical lines
        (x, y - size, x, y + size),  # Left vertical line
        (x + size, y - size, x + size, y + size),  # Right vertical line
        # Horizontal lines
        (x - size, y, x + size, y),  # Top horizontal line
        (x - size, y + size, x + size, y + size)  # Bottom horizontal line
    ]

    # Add offsets to each line's endpoints
    actions = []
    for (x0, y0, x1, y1), (dx, dy) in zip(lines, offsets):
        actions.append(Action("draw_line", [x0 + dx, y0 + dy, x1 + dx, y1 + dy]))

    return actions

def gen_initial_guess(initial: DrawState):
    return {
        "pos": [0.32, 0.24],  # Center of the drawing board (cm)
        "size": 0.1,          # Size of the hash symbol (cm)
        "point_offsets": [[0., 0.]] * 4  # 2D point offsets for the hash symbol (4 lines)
    }
```