
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 the two-digit integer $MM$, where both digits are equal, when multiplied by the one-digit integer $K$ (different from $M$ and only $1\leq K \leq 9$), it results in a three-digit number $NPK$. Identify the digit pairs $(M, K)$ that yield the highest value of $NPK$.

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