
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
Two parallel lines and a transversal intersect a circle, creating three chords of lengths $26, 38,$ and $34$. The lines are equally spaced, and the transversal cuts the $38$-length chord perpendicularly. What is the distance between the two parallel lines?
A) $7$
B) $10$
C) $14$
D) $15$
E) $16$

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