
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
A circle with its center on the side \( AC \) of an isosceles triangle \( ABC \) (\( AB = BC \)) is tangent to the sides \( AB \) and \( BC \). Find the radius of the circle if the area of triangle \( ABC \) is 25 and the ratio of the height \( BD \) to the side \( AC \) is \( 3:8 \).

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