
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 ${a_n}$ where $a_1=1$ and $a_{n-1}+a_{n}=( \frac {1}{3})^{n}$ (for $n\in\mathbb{N}^*$, $n\geq2$), and $T_{n}=a_{1}\cdot 3+a_{2}\cdot 3^{2}+…+a_{n-1}\cdot 3^{n-1}+a_{n}\cdot 3^{n}$. By analogy with the method for deriving the formula for the sum of a geometric series, find the value of $4T_{n}-a_{n}\cdot 3^{n+1}$.

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