
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 \( \triangle ABC \) be a triangle with \( AB = 9 \), \( BC = 10 \), and \( CA = 17 \). Let \( B' \) be the reflection of the point \( B \) over the line \( CA \). Let \( G \) be the centroid of triangle \( ABC \), and let \( G' \) be the centroid of triangle \( AB'C \). Determine the length of segment \( GG' \).

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