
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 a positive geometric sequence {a<sub>n</sub>} that satisfies a<sub>8</sub>\=a<sub>6</sub>+2a<sub>4</sub>, if there exist two terms a<sub>m</sub> and a<sub>n</sub> such that $$\sqrt {a_{m}a_{n}}$$\= $$\sqrt {2}$$a<sub>1</sub>, find the minimum value of $$\frac {1}{m}$$+ $$\frac {9}{n}$$.

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