
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 $x \in (0,2)$, $3^x > x^3$ is false if there exists $x\_0 \in (0,2)$ such that $3^{x\_0} \leq x\_0^3$;
(2) If $f(x) = 2^x - 2^{-x}$, then for all $x \in \mathbb{R}$, $f(-x) = -f(x)$;
(3) If $f(x) = x + \frac{1}{x+1}$, then there exists $x\_0 \in (0, +\infty)$ such that $f(x\_0) = 1$;
(4) In triangle $ABC$, if angle $A >$ angle $B$, then $\sin A > \sin B$.
Determine the true proposition(s).

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