
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
Consider a triangle $ABC$. The points $A'$, $B'$, and $C'$ divide the sides $AB$, $BC$, and $CA$ in the ratios $AA':A'B = BB':B'C = CC':C'A = 1:2$. In what ratio does the line $AB'$ divide the segments $BC'$ and $CA'$?

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