
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
(Ⅰ) Calculate: $$\frac{(\sqrt{2} + \sqrt{2}i)^{2}(4+5i)}{(5-4i)(1-i)}$$;  
(Ⅱ) In the complex plane, the parallelogram ABCD's vertices A, B, C correspond to the complex numbers i, 1, and 4+2i, respectively. Find the coordinates of vertex D and the length of the diagonals of the parallelogram.

Present the answer in LaTex format: \boxed{Your answer}
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