
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
Teacher Wu wants to assess the intelligence of two students, Xiao Ming and Xiao Gang. He thought of a positive integer $n$, and told both Xiao Ming and Xiao Gang the following two characteristics of $n$: ① $n$ is a three-digit number; ② $n$ is a perfect square. Teacher Wu also told Xiao Ming the sum of the digits of $n$, denoted as $s$, and told Xiao Gang the product of the digits of $n$, denoted as $p$. Xiao Ming and Xiao Gang had the following conversation:  
Xiao Gang: I know $s$ is a two-digit number. In fact, I know what $n$ is, and I also know that you don't know what $n$ is.  
Xiao Ming: Then now I know what $n$ is.  
Teacher Wu confirmed that Xiao Ming and Xiao Gang were both honest, and everything they said was based on evidence. So, what is $n$?

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