
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 $BD$ be the altitude of triangle $ABC$, and let $E$ be the midpoint of $BC$. Compute the radius of the circumcircle of triangle $BDE$ if $AB = 30 \text{ cm}$, $BC = 26 \text{ cm}$, and $AC = 28 \text{ cm}$.

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