
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
Consider the inequality $2y - 3x > \sqrt{9x^2}$. Determine under which of the following conditions the inequality holds true:
A) $y > 3x$ for all $x$
B) $y > 0$ for all $x$
C) $y > 3x$ for $x \geq 0$ and $y > 0$ for $x < 0$
D) $y < 0$ for $x \geq 0$ and $y < 3x$ for $x < 0$

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