
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, $ABC$ and $ACD$, are joined as shown. Squares are drawn on four of the sides. The areas of three of the squares are 25, 36, and 49 square units. What is the number of square units in the area of the fourth square, and what is the area of triangle $ACD$?

[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("$A$",(12,12),SE);
label("$B$",(0,12),SW);
label("$C$",(0,17),NNW);
label("$D$",(5.8,31),N);
label("49",((0,17)+(-14,22.8)+(-8.2,36.8)+(5.8,31))/4);
label("25",(-5/2,6+17/2));
label("36",(6,6));
[/asy]

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