
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 a rectangle of length $l$ and width $w$ such that $w = \sqrt{2} l$. A triangle is formed with the diagonal of the rectangle as its base and has unequal sides. The area of this triangle is equal to the area of the rectangle. Find the height of the triangle to the base (diagonal).
**A)** $\frac{2l\sqrt{3}}{3}$ **B)** $\frac{2l\sqrt{6}}{3}$ **C)** $\frac{l\sqrt{3}}{2}$ **D)** $\frac{l\sqrt{6}}{2}$ **E)** $2l$

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