
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 that the terms of a geometric sequence $\\{a\_n\\}$ are all positive, and $a\_1+a\_2= \frac {4}{9}$, $a\_3+a\_4+a\_5+a\_6=40$. Find the value of $\frac {a\_7+a\_8+a\_9}{9}$.

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