
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
A fenced area designed to contain sheep has an elliptic shape with a perimeter (approximated by Ramanujan's formula) of 200 units. The formula for the perimeter P of an ellipse with semi-major axis a and semi-minor axis b is given by: $P \approx \pi [3(a+b) - \sqrt{(3a + b)(a + 3b)}]$. What is the least possible area of this elliptic enclosure if a and b are integers?

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