
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
In trapezoid \(ABCD\), segments \(AB\) and \(CD\) are the bases. The diagonals of the trapezoid intersect at point \(K\). Find the area of triangle \(AKD\), given that \(AB = 27\), \(DC = 18\), \(AD = 3\), and \(BC = 6\sqrt{2}\).

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