
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
In the plane, the points $A(1, 2)$, $B(2, 1)$, $C(3, -3)$, and $D(0, 0)$ are given. They are the vertices of a convex quadrilateral $ABCD$. In what ratio does the intersection point of its diagonals divide the diagonal $AC$?

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