
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 vectors $\overrightarrow{a}=(m,n)$, $\overrightarrow{b}=(\cos\theta, \sin\theta)$, where $m$, $n$, $\theta \in \mathbb{R}$. If $|\overrightarrow{a}|=4|\overrightarrow{b}|$, determine the range of real number $\lambda$ for which $\overrightarrow{a} \cdot \overrightarrow{b} < \lambda^2$ always holds.

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