
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 alternate sides of 4 and 6 units. Compute the length of the chord that divides the hexagon into two quadrilaterals, one with alternate sides of 4 units and the other with alternate sides of 6 units. Provide your answer as a simplified fraction $m/n$ where $m$ and $n$ are relatively prime positive integers, and find $m+n$.

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