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Average Values from Tuple of Tuples

Write a Python function `average_tuple` that takes a tuple of tuples containing numerical values and returns a list of average values for each position across the tuples.

#### Example Usage
```python [main.nopy]
print(average_tuple(((10, 10, 10, 12), (30, 45, 56, 45), (81, 80, 39, 32), (1, 2, 3, 4))))
# Output: [30.5, 34.25, 27.0, 23.25]

print(average_tuple(((1, 1, -5), (30, -15, 56), (81, -60, -39), (-10, 2, 3))))
# Output: [25.5, -18.0, 3.75]

print(average_tuple(((100, 100, 100, 120), (300, 450, 560, 450), (810, 800, 390, 320), (10, 20, 30, 40))))
# Output: [305.0, 342.5, 270.0, 232.5]
```

#### Constraints
- The input will always be a tuple of tuples with at least one tuple.
- Each inner tuple will contain at least one numerical value.
def average_tuple(nums):
    """
    Calculate the average value for each position across all tuples.

    Args:
        nums (tuple of tuples): A tuple containing tuples of numerical values.

    Returns:
        list: A list of average values for each position.
    """
    # Placeholder for the solution
    pass
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