
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
Given \(\overrightarrow{AB} = 6 \vec{i} + \vec{j}\), \(\overrightarrow{BC} = x \vec{i} + y \vec{j}\), \(\overrightarrow{CD} = -2 \vec{i} - 3 \vec{j}\), and \(\overrightarrow{BC} \parallel \overrightarrow{DA}\). Find the relationship between \(x\) and \(y\).

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