
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 $PRS$, share a common hypotenuse $PR$. Squares are drawn on three sides of these triangles. The areas of three of the squares are 25, 49, and 64 square units. A circle is inscribed in triangle $PRS$. Find the number of square units in the area of the fourth square, assuming that the fourth square is drawn on side $PS$.

[asy]
defaultpen(linewidth(0.7));
draw((0,0)--(16,0)--(16,16)--(0,16)--cycle);
draw((3,16)--(3,19)--(0,19));
draw((0,16)--(0,22)--(16,16));
draw((0,22)--(7,37)--(16,16));
draw((7,37)--(28,44.4)--(32,21.6)--(16,16));
draw((0,22)--(-17,28.8)--(-10,43.8)--(7,37));
draw((0,16)--(-6,16)--(-6,22)--(0,22));
draw((1.2,19.5)--(1.7,20.7)--(0.5,21.2));
label("$P$",(16,16),SE);
label("$Q$",(0,16),SW);
label("$R$",(0,22),NNW);
label("$S$",(7,37),N);
label("49",(-11,30));
label("25",(-3,19));
label("64",(8,8));
[/asy]

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