
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
On each side of a right-angled triangle, a semicircle is drawn with that side as a diameter. The areas of the three semicircles are \( x^{2} \), \( 3x \), and 180, where \( x^{2} \) and \( 3x \) are both less than 180. What is the area of the smallest semicircle?

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