
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 plane α, there are five points A, B, C, D, E, where no three points are collinear. O is a point in space that satisfies $\overrightarrow{OA}=\frac{1}{2}\overrightarrow{OB}+x\overrightarrow{OC}+y\overrightarrow{OD}$ and $\overrightarrow{OB}=2x\overrightarrow{OC}+\frac{1}{3}\overrightarrow{OD}+y\overrightarrow{OE}$. Determine the value of $x+3y$.

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