
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 the sequence $\{a_n\}$ be defined by the general term $a_n = pn + q$ ($n \in \mathbb{N}^*$, $p > 0$), and the sequence $\{b_m\}$ be defined as follows: For a positive constant $m$, $b_m$ is the smallest value of $n$ that satisfies the inequality $a_n \geq m$.  
(I) If $p=2$, $q=-1$, find $b_1$, $b_2$, and the general formula for the sequence $\{b_m\}$.  
(II) Does there exist $p$ and $q$ such that $b_m = 3m + 2$ ($m \in \mathbb{N}^*$)? If so, find the range of values for $p$ and $q$; if not, explain why.

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