
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 cartesian coordinate system, a region termed "rhino's horn segment" is studied. This area is bounded by the quarter-circle in the first quadrant centered at origin $(0,0)$ with radius $4$, the half-circle in the first quadrant centered at $(0,2)$ with radius $2$, and the line segment connecting $(0,0)$ to $(4,0)$. Calculate the area of the "rhino's horn segment".

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