
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 $\{a\_n\}$, it satisfies $a\_1=1, a\_n+a_{n+1}=( \frac {1}{4})^{n}(n∈N^{}),, S\_n=a\_1+4⋅ a\_2+4^{2}⋅ a\_3+…+4^{n-1}a\_n$. By analogy with the method of deriving the formula for the sum of the first n terms of a geometric sequence in the textbook, find $S\_n- \frac {4^{n}}{5}a\_n=$ ___.

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