
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
Observe the following equations: $C_2^1 = C_1^1 + C_1$, $C_3^1 = C_2^1 + C_2$, $C_3^2 = C_2^2 + C_2^1$, $C_4^1 = C_3^1 + C_3$, $C_4^2 = C_3^2 + C_3^1$, $C_4^3 = C_3^3 + C_3^2$, ..., from these equations, infer a general conclusion: for any $n, r \in \mathbb{N}^+$ ($n > r$), $C_n^r =$ ___.

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