
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
If \( x \) is a four-digit integer in decimal notation, let \( T(x) \) denote the product of its digits, and \( S(x) \) denote the sum of its digits. Given that \( p \) is a prime number, \( T(x) = p^k \), and \( S(x) = p^p - 5 \), what is the smallest value of \( x \)?

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