
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 regular hexagon has a side length of 16 units. Find the lengths of the diagonal that connects two vertices that are two edges apart and the diagonal connecting opposite vertices. Express your answer in simplest radical form.

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