
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
$XYZ$ is a right triangle with $\angle YXZ = 90^\circ$, and $XY = 3$ cm, $XZ = 4$ cm. Line segment $\overline{YZ}$ is extended beyond $Z$ by its own length to point $W$, and $M$ is the midpoint of $\overline{XZ}$. Suppose $\overline{MW}$ meets $\overline{XY}$ at point $N$. Find the area of the triangle $MYN$ in square centimeters.

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