
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
We know the following to be true:

$\bullet$ 1.  \( X \) and \( M \) are integers with \( 1000 < X < 8000 \) and \( M > 1 \);

$\bullet$ 2.  \( X = M \times M^2 \).

What is the value of \( M \) for which \( X \) is a perfect square?

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