
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
Construct a symmetric trapezoid in which one of the parallel sides is equal in length to the sides. For the construction, the length of the sides and the distance from the intersection point of the diagonals to one end point of the other parallel side are given $(A M=a, A D=b)$.

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