
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 a triangle \(ABC\) with sides \(AB = 5\) and \(BC = 8\). The angle bisector of \(\angle B\) intersects the circumcircle of the triangle at point \(D\). 

a) It is known that the area of triangle \(ABD\) is 10. Find the area of triangle \(BCD\).  
b) Can the area of triangle \(ABD\) be 100?

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