
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 that non-zero vectors $\overrightarrow{OA}$, $\overrightarrow{OB}$ are not collinear, and $2 \overrightarrow{OP} = x \overrightarrow{OA} + y \overrightarrow{OB}$, if $\overrightarrow{PA} = \lambda \overrightarrow{AB} (\lambda \in \mathbb{R})$, determine the relation between $x$ and $y$.

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