
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
Real numbers $a$, $b$, and $c$ satisfy the inequalities $0 < a < 2$, $-2 < b < 0$, and $0 < c < 3$. Determine which of the following expressions is necessarily positive:
1. $b + a^2$
2. $b + ac$
3. $b + b^2$
4. $b + 3b^2$
5. $b + c$
**A)** $b + a^2$\
**B)** $b + ac$\
**C)** $b + b^2$\
**D)** $b + 3b^2$\
**E)** $b + c$

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