
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 $EFGH$, the sides $EF$ and $GH$ are equal. Trapezoid $EFGH$ is symmetric and the length of the top base $EF$ is $10$ units. The height from $EF$ to $GH$ is $6$ units. The length of the bottom base $GH$ exceeds that of $EF$ by $12$ units. Find the perimeter of trapezoid $EFGH$.
A) $32 + 6\sqrt{2}$
B) $30 + 12\sqrt{2}$
C) $32 + 12\sqrt{2}$
D) $34 + 12\sqrt{2}$
E) $32 + 18\sqrt{2}$

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