
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
Given the areas of three squares in the diagram, find the area of the triangle formed. The triangle shares one side with each of two squares and the hypotenuse with the third square.
[asy]
/* Modified AMC8-like Problem */
draw((0,0)--(10,0)--(10,10)--cycle);
draw((10,0)--(20,0)--(20,10)--(10,10));
draw((0,0)--(0,-10)--(10,-10)--(10,0));
draw((0,0)--(-10,10)--(0,20)--(10,10));
draw((9,0)--(9,1)--(10,1));
label("100", (5, 5));
label("64", (15, 5));
label("100", (5, -5));
[/asy]
Assume the triangle is a right isosceles triangle.

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