
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's consider the expression $x^3 - b$. If $x$ increases or decreases by a positive amount $a$, and $b$ increases by $a^2$, by what amount does the expression change?
A) $\pm 3x^2a + 3xa^2 \pm a^3$
B) $\pm 3x^2a - 3xa^2 \pm a^3$
C) $\pm 3x^2a + 3xa^2 \pm a^3 - a^2$
D) $3x^2a$
E) $- 3x^2a$

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