
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:
(1) $(C_{100}^2 + C_{100}^{97}) \div A_{101}^3$;
(2) $C_3^3 + C_4^3 + \ldots + C_{10}^3$;
(3) $\frac{C_{n+1}^m}{C_n^m} - \frac{C_n^{n-m+1}}{C_n^{n-m}}$.

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