
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
Two right triangles, $PQR$ and $PRS$, are joined as shown. Squares are constructed on four of their sides. The areas of three of the squares are 25, 64, and 49 square units. Determine the area of the fourth square. Assume $QR$ and $RS$ are the legs of their respective triangles, with $PR$ as the common hypotenuse.

Note that the diagram is not drawn to scale.

[asy]
defaultpen(linewidth(0.7));
draw((0,0)--(12,0)--(12,12)--(0,12)--cycle);
draw((2,12)--(2,14)--(0,14));
draw((0,12)--(0,17)--(12,12));
draw((0,17)--(5.8,31)--(12,12));
draw((5.8,31)--(24.8,37.2)--(31,18.2)--(12,12));
draw((0,17)--(-14,22.8)--(-8.2,36.8)--(5.8,31));
draw((0,12)--(-5,12)--(-5,17)--(0,17));
draw((1.2,16.5)--(1.7,17.7)--(0.5,18.2));
label("$P$",(12,12),SE);
label("$Q$",(0,12),SW);
label("$R$",(0,17),NNW);
label("$S$",(5.8,31),N);
label("64",((0,17)+(-14,22.8)+(-8.2,36.8)+(5.8,31))/4);
label("25",(-5/2,6+17/2));
label("49",(6,6));
[/asy]

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