
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:

(I) ${(\frac{|1−i|}{\sqrt{2}})}^{16} + \frac{{(1+2i)}^{2}}{1−i}$

(II) Given $\frac{1}{C_{5}^{m}} - \frac{1}{C_{6}^{m}} = \frac{7}{10C_{7}^{m}}$, find $C_{8}^{m}$.

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