
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
In a right-angled triangle, if the lengths of the two perpendicular sides are 6cm and 8cm, respectively, then the ratio of the radius of the inscribed circle to the radius of the circumscribed circle is ______.

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