
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 square $ABCD$, each side is 6 centimeters long. $E$ is a point on $\overline{CD}$ such that $DE = 2\text{ cm}$ and $EC = 4\text{ cm}$. Let $O$ be the intersection of $\overline{AC}$ and $\overline{BE}$. What is the ratio of $OC$ to $OA$?

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