
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 three strips of equal width 2 overlap at an angle of $\theta$, where $\theta \neq 0$ or $\pi/2$, in a three-dimensional arrangement where two strips are stacked one atop the other, and the third strip is placed perpendicularly across the middle of the other two, as viewed from above, calculate the area of the overlap of all three strips.

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