
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 the geometric sequence {a<sub>n</sub>} where a<sub>3</sub>\=4, and the sum of the first n terms S<sub>n</sub> satisfies $$\frac {S_{6}}{S_{3}}=9$$, find the value of $$a_{1}+ \frac {a_{2}}{2}+a_{3}+ \frac {a_{4}}{2}+a_{5}+ \frac {a_{6}}{2}+…+a_{19}+ \frac {a_{20}}{2}$$.

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