
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 shape was cut out from a regular hexagon as shown in the picture. The marked points on both the perimeter and inside the hexagon divide the respective line segments into quarters.

What is the ratio of the areas of the original hexagon to the cut-out shape?

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