
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
The circle is tangent to the sides \(AC\) and \(BC\) of triangle \(ABC\) at points \(A\) and \(B\) respectively. On the arc of this circle, lying inside the triangle, there is a point \(K\) such that the distances from it to the sides \(AC\) and \(BC\) are 6 and 24 respectively. Find the distance from point \(K\) to the side \(AB\).

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