
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
Five circles are consecutively tangent to one another and to two parallel lines \( L_1 \) and \( L_2 \). If the radius of the smallest circle is 6 and that of the largest circle is 30, find the radius of the third circle from the smallest (middle circle), assuming that the radii of the circles increase by a constant difference.
- **A**) 16
- **B**) 17
- **C**) 18
- **D**) 19
- **E**) 20

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