
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 circle of radius $3$ cut into three equal arcs, and then these arcs used to form a triangular shape within a square whose side equals the diameter of the circle, determine the ratio of the area of the triangular shape to the area of the original circle.

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