
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
In trapezoid EFGH, sides EF and GH are equal. It is known that EF = 12 units and GH = 10 units. Additionally, each of the non-parallel sides forms a right-angled triangle with half of the difference in lengths of EF and GH and a given leg of 6 units. Determine the perimeter of trapezoid EFGH.

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