
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 square and an equilateral triangle of equal heights are placed side by side with both bases on the $x$-axis. The lower right vertex of the square and the lower left vertex of the triangle are at $(14, 0)$. The side of the square on the $x$-axis equals 14 units, and each side of the triangle equals 18 units. A segment is drawn from the top left vertex of the square to the farthest vertex of the triangle. Calculate the area of the shaded region created by this segment within the triangle.

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