
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 function f(x) = lg $\frac{2x^2 + bx + c}{x^2 + 1}$, and the solution set of the inequality bx² + 3x + c ≥ 0 with respect to x is set A = {x|$-\frac{1}{2} \leq x \leq 2$}.
(I) Find the values of b and c.
(II) Let M = {m|there exists a t in A such that f(t) = m holds true}, find the set M.

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