
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 vectors $\overset{⇀}{OA}$ and $\overset{⇀}{OB}$, both with a length of $2$, and an angle of $\dfrac{\pi}{3}$ between them. Point $C$ lies on the minor arc $AB$ of the circle with center $O$, and $\overset{⇀}{OC}=m\overset{⇀}{OA}+n\overset{⇀}{OB}$. Determine the maximum value of $m+n$.

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