
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 the diagram, $AB$ is perpendicular to $BC$, and $CD$ is perpendicular to $AD$. Also, $AC = 625$ and $AD = 600$. If $\angle BAC = 2 \angle DAC$, what is the length of $BC$?

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