
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 rhombus with a side length of 6 cm is inscribed in a right triangle with a $60^{\circ}$ angle such that the $60^{\circ}$ angle is common to both the rhombus and the triangle, and all vertices of the rhombus lie on the sides of the triangle. Find the sides of the triangle.

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