
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
The height of a rhombus, drawn from the vertex of its obtuse angle, divides the side of the rhombus in the ratio $1:3$, measured from the vertex of its acute angle. What fraction of the area of the rhombus is occupied by the area of a circle inscribed in it?

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