
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
When the two-digit integer $MM$, with equal digits, is multiplied by the one-digit integer $N$, and the result is the three-digit integer $NPP$, determine the smallest possible value of $NPP$ where $P$ and $M$ are digits.

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