
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]


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In an arithmetic progression $\{a_n\}$, it is given that $$\frac {a_{1}+a_{2}+a_{3}+a_{4}+a_{5}+a_{6}}{6} = \frac {a_{3}+a_{4}}{2}.$$ What similar conclusion can we draw for a geometric progression with positive terms $\{b_n\}$?

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