
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
Let \( f(x) \) be an arbitrary function and \( n \in \mathbf{N}_{+} \). Then
$$
f(x+n)=f(x)+C_{n}^{1} \Delta f(x)+C_{n}^{2} \Delta^{2} f(x)+\cdots+C_{n}^{n} \Delta^{n} f(x) .
$$

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