
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 the diagram, the grid is made up of squares. A larger right triangle (points A at bottom left, B at bottom right, C at top right of the grid) is cut out. Within the larger triangle, a smaller triangle (points D at bottom left, E 12 units to the right along the base from D, F 3 units up from E) is shaded. Calculate the area of the shaded region. The base of the larger triangle is the width of the grid and its height is one unit less than the height of the grid. The dimensions of the entire grid are 15 units by 5 units.

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