
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 sequence $\{a_n\}$ have a sum of the first $n$ terms denoted by $S_n$, and for any positive integer $n$, it holds that $a_n=5S_n+1$.

(Ⅰ) Find the general formula for the sequence $\{a_n\}$;

(Ⅱ) Let $b_n=\log_{4}|\frac{1}{a_n}|$, calculate the sum of the first $n$ terms, $T_n$, for the sequence $\left\{ \frac{1}{b_n \cdot b_{n+1}} \right\}$.

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