
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 the following propositions:

(1) For all $x \in \mathbb{R}$, $x^3 > x^2$;

(2) There exists an $x\_0 \in \mathbb{R}$ such that $\sin(3x\_0) = 3\sin(x\_0)$;

(3) The negation of the proposition "There exists an $x\_0 \in \mathbb{R}$ such that $x\_0^2 - 2x\_0 > 0$" is "There exists an $x\_0 \in \mathbb{R}$ such that $x\_0^2 - 2x\_0 \leq 0$";

(4) The proposition "Some triangles are right triangles" is a universal statement and is true.

Identify the false proposition(s) by filling in the blank(s) with the appropriate proposition number(s).

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