
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
Given are circles \( k_{1}, k_{2}, k_{3}, \) and \( k_{4} \) with centers \( S_{1}, S_{2}, S_{3}, \) and \( S_{4} \) respectively. Circle \( k_{1} \) externally touches all other circles, the radius of circle \( k_{1} \) is \( 5 \, \mathrm{cm} \). The distance between the centers \( S_{2} \) and \( S_{4} \) is \( 24 \, \mathrm{cm} \) and the quadrilateral \( S_{1} S_{2} S_{3} S_{4} \) is a rhombus.

Determine the radii of circles \( k_{2}, k_{3}, \) and \( k_{4} \).

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