
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 sequence $\{a\_n\}$ satisfies $a\_1=1$, $a\_n+a_{n+1}=( \frac {1}{3})^{n}$, $S\_n=a\_1+3a\_2+3^{2}a\_3+…+3^{n-1}a\_n$, using a method similar to the sum of a geometric series, find $4S\_n-3^{n}a\_n$.

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