
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
(1) Calculate the complex number $z=i+i^2+i^3+i^4$;
(2) Calculate $\left( \binom{100}{2} + \binom{100}{97} \right) \div A_{101}^3$;
(3) Calculate $\binom{3}{3} + \binom{4}{3} +\ldots+ \binom{10}{3}$.

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