
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 $\{a_n\}$ be a geometric sequence with a common ratio greater than 1, and let $S_n$ be the sum of the first $n$ terms of $\{a_n\}$. It is known that $S_3=7$, and $a_1$, $a_2$, $a_3-1$ form an arithmetic sequence.  
(1) Find the general formula for the sequence $\{a_n\}$.  
(2) If $b_n=\log_{4}a_{2n+1}$, for $n=1,2,3,\ldots$, find the sum: $$\frac {1}{b_{1}b_{2}}+ \frac {1}{b_{2}b_{3}}+ \frac {1}{b_{3}b_{4}}+\ldots+ \frac {1}{b_{n-1}b_{n}}$$.

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