
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 \( k \) is a positive integer, the quadratic equation
\[ (k-1)x^2 - px + k = 0 \]
has two positive integer roots. Find the value of \( k^{kp} \left(p^p + k^k\right) \).

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