
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 the angle between the unit vectors $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ is $α$, and $\cos α= \frac{1}{3}$, find the value of $\cos β$, where $β$ is the angle between vectors $\overrightarrow{a}=3 \overrightarrow{e_{1}}-2 \overrightarrow{e_{2}}$ and $\overrightarrow{b}=3 \overrightarrow{e_{1}}- \overrightarrow{e_{2}}$.

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