
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
Let \(ABCD\) be an isosceles trapezoid with parallel bases \(AB=1\) and \(CD=2\) and height 1. Find the area of the region containing all points inside \(ABCD\) whose projections onto the four sides of the trapezoid lie on the segments formed by \(AB, BC, CD,\) and \(DA\).

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