
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
The area of a triangle is divided into three triangles and a quadrilateral by drawing two lines from vertices to their opposite sides, with the areas of the three triangles being 4, 9, and 9, respectively. Calculate the area of the shaded quadrilateral.

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