
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
Four congruent isosceles right triangles are positioned such that their hypotenuses form a larger square, while the other two sides of each triangle form the sides of an inner square. The area of the outer square is 2 times that of the inner square. Determine the ratio of the length of the longer side (hypotenuse) of each triangle to the length of its shorter side.
A) $\sqrt{3}$
B) $1$
C) $\sqrt{2}$
D) $2$

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