
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 geometric sequence with positive terms $\{a_n\}$, it is given that $a_{2017} = a_{2016} + 2a_{2015}$. If $a_m a_n = 16a_1^2$, then the minimum value of $\left( \frac{4}{m}+ \frac{1}{n} \right)$ equals

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