
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 geometric sequence $\{a_n\}$ with positive terms, where $a_5$, $\frac{1}{2}a_7$, $a_6$ form an arithmetic sequence, find the value of $\frac{a_1+a_2+a_3}{a_2+a_3+a_4}$.

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