
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
Let the sum of the first n terms of the sequence {a_n} be S_n, a_1=1, and 2S_n=a_{n+1}-1 (n∈ N*). If for any positive integer n, the equation a_1b_n+a_2b_{n-1}+a_3b_{n-2}+...+a_nb_1=3^n-n-1 holds, then determine all positive integers n satisfying the equation b_1+b_2+b_3+...+b_n=a_n.

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