
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 vectors $\overrightarrow{a}=(\cos 40^{\circ},\sin 40^{\circ})$, $\overrightarrow{b}=(\sin 20^{\circ},\cos 20^{\circ})$, and $\overrightarrow{u}= \sqrt {3} \overrightarrow{a}+λ \overrightarrow{b}$ (where $λ∈R$), find the minimum value of $|\overrightarrow{u}|$.

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