
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 base of an isosceles triangle is $20$ inches. Two lines are drawn parallel to the base, terminating at the other two sides, which divide the triangle into three regions of equal area. Find the difference in lengths between the two parallel lines.
A) $\frac{20\sqrt{3}}{3}$ inches
B) $\frac{40(\sqrt{6} - \sqrt{3})}{3}$ inches
C) $\frac{20(\sqrt{6} - \sqrt{3})}{3}$ inches
D) $10\sqrt{3}$ inches

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