
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
In an isosceles triangle $PQR$ with $PQ = PR$, the altitude $PS$ divides the base $QR$ equally. If $PQ = PR = 41$ units and the length of the base $QR$ is 18 units, determine the area of $\triangle PQR$.

[asy]
draw((0,0)--(18,0)--(9,40)--cycle,black+linewidth(1));
draw((9,40)--(9,0),black+linewidth(1)+dashed);
draw((9,0)--(9,1)--(8,1)--(8,0)--cycle,black+linewidth(1));
draw((8.5,-4)--(0,-4),black+linewidth(1));
draw((8.5,-4)--(0,-4),EndArrow);
draw((9.5,-4)--(18,-4),black+linewidth(1));
draw((9.5,-4)--(18,-4),EndArrow);
label("$P$",(9,40),N);
label("$Q$",(0,0),SW);
label("$R$",(18,0),SE);
label("$S$",(9,0),S);
label("41",(0,0)--(9,40),NW);
label("41",(9,40)--(18,0),NE);
label("18",(9,-4));
[/asy]

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