
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
Calculate the following expressions:

(1) $(-\frac{1}{2}+\frac{\sqrt{3}}{2}i)(2-i)(3+i)$;

(2) $\frac{(\sqrt{2}+\sqrt{2}i)^{2}(4+5i)}{(5-4i)(1-i)}$.

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