
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 an geometric sequence {$a_n$} with the sum of its first $n$ terms denoted as $S_n$, all terms are positive numbers. It is known that $3a_1$, $\frac {1}{2}a_3$, and $2a_2$ form an arithmetic sequence. Then calculate the value of $\frac {S_{11}-S_{9}}{S_{7}-S_{5}}$.

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