
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 trapezoid with integer sides has an inscribed circle. The median line of the trapezoid divides it into two parts, the areas of which are 15 and 30. Find the radius of the inscribed circle.

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