
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 right triangle has acute angles of $60^{\circ}$ and $30^{\circ}$. Two congruent circles are inscribed in the triangle, touching the hypotenuse, each other, and one of the legs. How many times is the smaller leg of the triangle the radius of the circles?

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