
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 that the sum of the first $n$ terms of a geometric sequence $\{a_n\}$ is $S_n$, and $S_4 = a_5 - a_1$.  
(1) Find the value of the common ratio $q$ of the sequence $\{a_n\}$.  
(2) Let $b_n = \log_{2}a_{n+1}$, and the sum of the first $n$ terms of the sequence $\{b_n\}$ is $T_n$. If $T_4 = 2b_5$, find the sum of the first 9 terms of the sequence $\left\{ \frac {1}{b_{n}b_{n+1}}\right\}$.

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