
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 sequence {a<sub>n</sub>} is a decreasing geometric sequence and satisfies the conditions $$a_{2}a_{7}= \frac {1}{2}$$ and $$a_{3}+a_{6}= \frac {9}{4}$$, find the maximum value of a<sub>1</sub>a<sub>2</sub>a<sub>3</sub>…a<sub>2n</sub>.

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