
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 legs of a right triangle are 9 cm and 12 cm. Find the distance between the incenter (the point of intersection of its angle bisectors) and the centroid (the point of intersection of its medians).

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