
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 leg of an isosceles triangle is $10 \text{ cm}$, and the base is $12 \text{ cm}$. Tangents are drawn to the circle inscribed in the triangle, parallel to the height of the triangle, and they cut off two right triangles from the given triangle. Find the lengths of the sides of these right triangles.

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