
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
Let $\triangle ABC$ be a right triangle such that $B$ is a right angle. A circle with diameter $BC$ intersects side $AC$ at $D$ and intersects side $BC$ at point $E$ where $E$ is not equal to $B$ or $C$. Given that the area of $\triangle ABC$ is $200$ and $AC = 30$, find the length of $BD$.

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