
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 two planar vectors $\overrightarrow{OA}$ and $\overrightarrow{OB}$, both of length $1$, with an angle of ${120}^{{}^\circ }$ between them. If $\overrightarrow{OC}=x\overrightarrow{OA}+y\overrightarrow{OB}$, where $x,y\in R$, determine the maximum value of $x+y$.

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