
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 the plane vectors $\overrightarrow{a}, \overrightarrow{b}$ with magnitudes $|\overrightarrow{a}|=2$ and $|\overrightarrow{b}|=\frac{1}{3}|\overrightarrow{a}|$, as well as the magnitude of the difference between them $|\overrightarrow{a}-\frac{1}{2}\overrightarrow{b}|=\frac{\sqrt{43}}{3}$, determine the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$.

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