
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
Given a square  $ABCD$  with side length  $6$ . We draw line segments from the midpoints of each side to the vertices on the opposite side. For example, we draw line segments from the midpoint of side  $AB$  to vertices  $C$  and  $D$ . The eight resulting line segments together bound an octagon inside the square. What is the area of this octagon?

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