
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 triangle \( A B C \), the base of the height \( C D \) lies on side \( A B \), and the median \( A E \) is equal to 5. The height \( C D \) is equal to 6.

Find the area of triangle \( A B C \), given that the area of triangle \( A D C \) is three times the area of triangle \( B C D \).

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