
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 $\{a_n\}$, there exist two terms $a_m$ and $a_n$ such that $\sqrt {a_m a_n}=4a_1$, and $a_6=a_5+2a_4$. Find the minimum value of $\frac {1}{m}+ \frac {4}{n}$.

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