
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
Let  $G$  be the centroid of triangle  $ABC$  with  $AB=13,BC=14,CA=15$ . Calculate the sum of the distances from  $G$  to the three sides of the triangle.

Note: The *centroid* of a triangle is the point that lies on each of the three line segments between a vertex and the midpoint of its opposite side.

*2019 CCA Math Bonanza Individual Round #11*

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