
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 circle is inscribed in a trapezoid. Find the area of the trapezoid if the lengths of one of the bases \(a\) and the segments \(b\) and \(d\) (into which the point of tangency divides one of the non-parallel sides, with segment \(b\) adjacent to the given base) are known.

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