
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, then
\[ 
\Delta^{n} f(x) = C_{n}^{0} f(x+n) - C_{n}^{1} f(x+n-1) + C_{n}^{2} f(x+n-2) - \cdots + (-1)^{n} C_{n}^{n} f(x).
\]

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