
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 sequence ${a_n}$, $a_1=2$, $a_{n+1}-2a_n=0 (n \in N^*)$, $b_n$ is the arithmetic mean of $a_n$ and $a_{n+1}$, and $S_n$ is the sum of the first $n$ terms of the sequence ${b_n}$. Find $S_6$.

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