
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 perimeter of triangle \(ABC\) is 24 cm, and the segment connecting the centroid (intersection point of the medians) with the incenter (intersection point of the angle bisectors) is parallel to side \(AC\). Find the length of \(AC\).

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