
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
Two strips of width 1 and 2 overlap at an angle of $\beta$. Calculate the area of the overlap (shaded region), which is defined by the boundaries where these strips intersect, forming a kite-shaped region.
A) $\sin \beta$
B) $\frac{1}{\sin \beta}$
C) $\frac{1}{1 - \cos \beta}$
D) $\frac{1}{\sin^2 \beta}$
E) $\frac{1}{(1 - \cos \beta)^2}$

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