
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 \( P(n) \) denote the product of the digits of the integer \( n \) raised to the power of 2, and \( S(n) \) denote the sum of the digits of \( n \). Suppose \( N \) is a two-digit number such that \( N = P(N)^2 + S(N) \). What is the tens digit of \( N \)?

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