
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
Given isosceles trapezoid \(ABCD\) with \(M\) as the intersection point of its diagonals. It is known that the lateral side \(AB\) is perpendicular to the bases \(AD\) and \(BC\), and that a circle can be inscribed in the trapezoid. Find the area of triangle \(DCM\) if the radius of this inscribed circle is \(r\).

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