
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
On the base $AD$ of trapezoid $ABCD$, a point $K$ is selected. It turns out that $AB = BK$ and $KC = CD$. It is given that the ratio of the areas of triangles $ABK$ and $KCD$ is param1, and the radii of the circles inscribed in triangles $ABK$ and $KCD$ are respectively param2 and param3. Find the radius of the circle inscribed in triangle $KBC$.

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