
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
\[10.6 \frac{1+3i}{1-3i} + \frac{1-3i}{1+3i} + \frac{1}{8i^3} \]

\[10.7 \left(\frac{-1-i\sqrt{3}}{2}\right)^3 + \left(\frac{-1+i\sqrt{3}}{2}\right)^3 \]

\[10.8 \left( -2(1+i)^3 + \frac{31-17i}{4-3i} \right) \frac{1+i}{6} -1 \]


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