
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
Triangle ABC has a right angle at B. Point D is the foot of the altitude from B, with AD=5, and DC=6. What is the area of $\triangle ABC$?
A) $\frac{11\sqrt{10}}{2}$
B) $\frac{11\sqrt{30}}{2}$
C) $\frac{11\sqrt{15}}{2}$
D) $11\sqrt{30}$
E) $5\sqrt{30}$

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