
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
In a positive geometric sequence $\{a_n\}$, it is given that $a_{2016} = a_{2015} + 2a_{2014}$. If $a_m a_n = 16a_1^2$, calculate the minimum value of $\frac{4}{m} + \frac{1}{n}$.

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