
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
Given that \( n \) is a positive integer and \( x \) a real number, compute the sum: 
\[ \sum_{k=0}^{n} k^{2} \cdot C_{n}^{k} \cdot x^{k} \cdot(1-x)^{n-k}. \]

(Please write the answer in its simplest form.)

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