
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
Simplify the following complex numbers given in polar form:

1. \( 10.25 \sqrt{6}\left(\cos 160^{\circ}+i \sin 160^{\circ}\right) \div \sqrt{3}\left(\cos 40^{\circ}+i \sin 40^{\circ}\right) \)

2. \( 10.268\left(\cos \left(-105^{\circ}\right)+i \sin \left(-105^{\circ}\right)\right) \div (-0.5 \sqrt{3} - 0.5 i) \)

Raise the following complex numbers to the given powers:

3. \( 10.27 \left(\sqrt{2}\left(\cos \frac{5 \pi}{18}+i \sin \frac{5 \pi}{18}\right)\right)^{6} \)

4. \( 10.28 (-1+\sqrt{3} i)^{9} \)

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