
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 rectangle \(ABCD\) is inscribed in a segment with a \(120^{\circ}\) arc and height \(h\), where the ratio of \(AB\) to \(BC\) is \(1:4\) (with \(BC\) lying on the chord). Find the area of the rectangle.



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