
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
Three coplanar squares with side lengths of 3, 6, and 9 units, respectively, are arranged consecutively so that one side of each square lies on line CD. A line segment connects the bottom left corner of the smallest square to the upper right corner of the largest square. Determine the areas of the shaded trapezoid and the triangle formed by the line segment and the rightmost side of the largest square.

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