
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 of length 4 and three consecutive sides of length 6. The chord of the circle that divides the hexagon into two polygons, one with sides of lengths 4, 4, 4, and the other with sides of lengths 6, 6, 6, is inclined at an angle of 80 degrees to one side of the hexagon. Find the length of the chord, expressed in simplest radical form.

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