
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
An equilateral triangle has a side length of 6 units. Calculate the ratio of its area to the perimeter, and then find the sum of this ratio and the height of the triangle. Express your final answer in simplest radical form.

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