
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
On the sides \(BC\), \(CA\), and \(AB\) of triangle \(ABC\), points \(A_1\), \(B_1\), and \(C_1\) are chosen respectively. The medians \(A_1A_2\), \(B_1B_2\), and \(C_1C_2\) of triangle \(A_1 B_1 C_1\) are respectively parallel to the lines \(AB\), \(BC\), and \(CA\). In what ratio do the points \(A_1\), \(B_1\), and \(C_1\) divide the sides of triangle \(ABC\)?

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