
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

Using the expansion of \((1+i)^{n}\) by the binomial theorem, find:

a) \(C_{100}^{0} - C_{100}^{2} + C_{100}^{4} - \ldots + C_{100}^{100}\)

b) \(C_{99}^{1} - C_{99}^{3} + C_{99}^{5} - \ldots - C_{99}^{99}\)

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