
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 $f(x) = 2x^2 + 3x + 1$. Determine for which of the following conditions the inequality $|2f(x) - 4| < a$ holds whenever $|x + 1| < b$, where $a > 0$ and $b > 0$.
A) $b \leq \sqrt{a/2}$
B) $b > a$
C) $b^2 \leq a$
D) $b$ is any positive number as long as $a > 2$
E) $a \leq b$

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