
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 $|\vec{OA}|=1$, $|\vec{OB}|=2$, and $\angle AOB = \frac{2\pi}{3}$, $\vec{OC} = \frac{1}{2}\vec{OA} + \frac{1}{4}\vec{OB}$, find the magnitude of the angle between $\vec{OA}$ and $\vec{OC}$.

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