
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
In triangle $ABC$, side lengths opposite to angles $A$, $B$, and $C$ are a, b, and c, respectively. Vector $\overrightarrow{m} = (\cos A, \cos B)$ is collinear with vector $\overrightarrow{n} = (a, 2c - b)$.  
(I) Find the magnitude of angle $A$.  
(II) Given a geometric progression $\{a_n\}$ where $a_1\cos A = 1$ and $a_4 = 16$, and let $b_n = \log_2 a_n \cdot \log_2 a_{n+1}$, find the sum $S_n$ of the reciprocals $\left\{\frac{1}{b_n}\right\}$ for the first $n$ terms.

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