
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 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 the sequence $\{a\_n\}$;
(II) Let $b\_n = \log\_2 a\_n (n \in \mathbb{N}^*)$, find the smallest integer $n$ such that $b\_1 + b\_2 + \dots + b\_n > 45$.

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