
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
$$10.30 \frac{\left(\cos 72^{\circ} + i \sin 72^{\circ}\right) \left(\cos 41^{\circ} + i \sin 41^{\circ}\right)^{2}}{\cos 19^{\circ} + i \sin 19^{\circ}}.$$

$$10.31(6 - 6i)^{2}\left(\frac{1}{4} - \frac{\sqrt{3}}{4} i\right)^{3}.$$

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