
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
A right triangular pyramid $WXYZ$ has base $WXY$, where $WX = XY = 4$ cm, and $WY = 4\sqrt{2}$ cm, forming a right angle at $W$. The altitude $WZ$ from $W$ to the apex is perpendicular to the base and measures $8$ cm. Point $P$ lies on $XZ$, one quarter of the way from $X$ to $Z$; point $Q$ lies on $YZ$, one half of the way from $Y$ to $Z$; and point $R$ lies on $WZ$, three quarters of the way from $W$ to $Z$. Determine the area, in square centimeters, of triangle $PQR$.
A) $\frac{3\sqrt{185}}{2}$
B) $\frac{3\sqrt{195}}{2}$
C) $\frac{3\sqrt{205}}{2}$
D) $\frac{3\sqrt{215}}{2}$

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