
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 that $a > b > 0$, $c > 0$, and $d \neq 0$, determine which of the following inequalities is not always true:
1. $a + cd > b + cd$
2. $a^2 - cd > b^2 - cd$
3. $a/c > b/c$
4. $(a + d)^2 > (b + d)^2$
5. $\sqrt{a} \cdot d^2 > \sqrt{b} \cdot d^2$
A) $a + cd > b + cd$
B) $a^2 - cd > b^2 - cd$
C) $a/c > b/c$
D) $(a + d)^2 > (b + d)^2$
E) $\sqrt{a} \cdot d^2 > \sqrt{b} \cdot d^2$

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