
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 triangle $\triangle ABO$, it is known that $OA=OB=1$, $\angle AOB=\frac{π}{3}$. If $OC$ intersects segment $AB$ at point $P$, and satisfies $\overrightarrow{OC}=\lambda \overrightarrow{OA}+μ\overrightarrow{OB}$, $|\overrightarrow{OC}|=\sqrt{3}$, determine the maximum value of $\lambda +\mu$.

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