
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 a sequence $\{a_n\}$ where $a_1=1$ and $a_{n+1}=c - \frac{1}{a_n}$.
(I) Let $c = \frac{5}{2}$, and let $b_n = \frac{1}{a_n - 2}$, find the general formula for the sequence $\{b_n\}$.
(II) Find the range of values for $c$ that make the inequality $a_n < a_{n+1} < 3$ always true.

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