
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) For any $f(x) \in p[x]$ and a constant $a$, $C_{k}\langle a f(x) \rangle = a C_{k}\langle f(x) \rangle$.

(2) For any $f(x), g(x) \in p[x]$, $C_{k}\langle f(x) \pm g(x) \rangle = C_{k}\langle f(x) \rangle \pm C_{k}\langle g(x) \rangle$; $C_{k}\langle f(x) g(x) \rangle = \sum_{i=0}^{k} C_{i}\langle f(x) \rangle \cdot C_{k-i}\langle g(x) \rangle$.

(3) For any positive integers $n, k$ and $f(x), g(x) \in p[x]$, when $n > k$, $C_{k}\langle f(x) \rangle = C_{n}\langle x^{n-k} f(x) \rangle$, $C_{k}\langle f(x) \rangle = C_{k}\langle f(x) + x^{n} g(x) \rangle$.

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