
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 alternating side lengths of 4 and 7. Calculate the length of a chord that divides the hexagon into two trapezoids, one with sides of length 4 and the other with sides of length 7. Express the length of the chord as a fraction $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, and find $m+n$.

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