
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
Triangle $MNP$ is similar to triangle $XYZ$. If $MN = 8$, $NP = 16$, and $YZ = 24$ units, what is the length of segment $XY$? Moreover, if segment $XY$ is also the side of a square, what is the area of that square?

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