
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
Given a larger equilateral triangle with a side length of 4 units, a smaller equilateral triangle has an area that is one-third the area of the larger triangle. Calculate the radius of the circle inscribed within the smaller triangle.
A) \( \frac{1}{2} \) units
B) \( \frac{2}{3} \) units
C) \( \frac{3}{4} \) units
D) \( 1 \) unit

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