
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 a sequence $\{a_n\}$ whose sum of the first $n$ terms is $S_n$, and $S_n+ \frac {1}{3}a_n=1(n\in\mathbb{N}_{+}).$

(Ⅰ) Find the general formula for the sequence $\{a_n\}$;  
(Ⅱ) Let $b_n=\log _{4}(1-S_{n+1})(n\in\mathbb{N}_{+})$, $T_n= \frac {1}{b_1b_2}+ \frac {1}{b_2b_3}+\ldots+ \frac {1}{b_nb_{n+1}}$, find the smallest positive integer $n$ such that $T_n\geqslant \frac {504}{1009}$.

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