
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 $\overrightarrow{a}$ is an arbitrary vector forming an angle of $60^{\circ}$ with the unit vector $\overrightarrow{b}$, determine the minimum value of the function $f(\lambda)=\left|\lambda \overrightarrow{a}- \overrightarrow{b}\right| \cdot \frac{\left|\left( \sqrt{3} \overrightarrow{a}\right) \cdot \overrightarrow{b}\right|}{\left| \overrightarrow{a}\right|}$ for $\lambda > 0$.

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