
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]


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Given the sequence $\{a\_n\}$ that satisfies $a_{n+1}=2a_{n}$, and $a_{1}$, $a_{2}+1$, $a_{3}$ form an arithmetic sequence.
(I) Find the general term formula for $\{a\_n\}$;
(II) Let $S_{n}$ denote the sum of the first $n$ terms of the sequence $\{\log_{2}a_{n}\}$. Find the smallest positive integer value of $n$ that makes the inequality $S_{n} > 45$ true.

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