
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 the geometric sequence ${a_{n}}$, all terms are positive, and $a_{1}$, $\frac {1}{2}a_{3}$, $2a_{2}$ form an arithmetic sequence. Find the value of $\frac {a_{6}+a_{8}+a_{10}}{a_{7}+a_{9}+a_{11}}$.

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