
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
For a class project on geometry, Theo decides to create a model of a kite to study its properties. He constructs two versions of the kite, a small one and a large one, using points arranged two inches apart each. The small kite has vertices on a grid at the coordinates (0,6), (3,10), (6,6), and (3,0).

The large kite has double the dimensions of the small kite in terms of the spacing of grid points.

Calculate the area of the small kite in square inches.

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