
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
A hexagon inscribed in a circle has three consecutive sides, each of length 4, and three consecutive sides, each of length 7. The chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 4, and the other with three sides each of length 7, has length equal to $p/q$, where $p$ and $q$ are relatively prime positive integers. Find $p + q$.

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