
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
In the configuration described, five circles are tangent to one another consecutively and to the lines \(L_1\) and \(L_2\). The radius of the largest circle is 24 and that of the smallest circle is 12. Determine the radius of the middle circle.
A) \( 15 \)
B) \( 16 \)
C) \( 12\sqrt{2} \)
D) \( 18 \)
E) \( 20 \)

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