
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
In a diagram, a grid consists of a larger rectangle subdivided into smaller rectangles and right triangles. The entire grid's dimensions are 10 units wide and 5 units high. Part of the grid includes a shaded region where an unshaded right triangle and a trapezoid have been cut out. The triangle has a base of 3 units along the bottom and a height of 2 units, while the trapezoidal section starts 3 units from the left, with a height of 3 units, and has a top base of 3 units and a bottom base of 6 units. Calculate the area of the shaded region.

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