
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 $\log_M (N^2) = 2\log_N M$, given that $M \neq N$, $M, N > 1$ and neither $M$ nor $N$ are equal to 1, determine the value of $MN$.
A) $\frac{1}{2}$
B) $1$
C) $2$
D) $10$
E) A number greater than 2 and less than 10

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