
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
An equilateral triangle has a side length of 4 units. Inside this triangle, a smaller equilateral triangle is drawn such that its area is one-third of the larger triangle. Adjacent to the larger triangle, a rectangle is constructed with a length equal to double the side of the smaller triangle and a width half of the smaller triangle's side. Calculate the total area of the compound shape formed by the larger triangle and the rectangle.
A) \( 4\sqrt{3} + \frac{16}{3} \text{ square units} \)
B) \( 3\sqrt{3} + 5 \text{ square units} \)
C) \( 6\sqrt{3} + 4 \text{ square units} \)
D) \( 5\sqrt{3} + \frac{13}{3} \text{ square units} \)

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