
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
A large isosceles triangle has a base length of $2$ and a height of $1$. Inside it, two smaller congruent isosceles triangles are constructed such that each has its base along the base of the larger triangle, divided equally, and each has a height that is half that of the larger triangle. If the sum of the areas of the two smaller triangles is half the area of the larger triangle, what is the length of one of the congruent sides of the smaller isosceles triangles?
A) $\frac{\sqrt{3}}{4}$  
B) $\frac{\sqrt{2}}{3}$  
C) $\frac{2}{3}$  
D) $\frac{\sqrt{2}}{2}$  
E) $\frac{\sqrt{3}}{2}$

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