
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
Two circles with radii 3 and 4, and a distance of 5 between their centers, intersect at points \(A\) and \(B\). A line through point \(B\) intersects the circles at points \(C\) and \(D\), such that \(CD = 8\) and point \(B\) lies between points \(C\) and \(D\). Find the area of triangle \(ACD\).

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