
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 four propositions:
$(1)$ The negation of the proposition "$\forall x \in \mathbb{R}$, $\cos x > 0$" is "$\exists x \in \mathbb{R}$, $\cos x \leq 0$".
$(2)$ Lines $a$, $b$, and $c$ are three lines in space. The necessary and sufficient condition for $a \parallel b$ is $a \perp c$ and $b \perp c$.
$(3)$ In $\triangle ABC$, if $\angle A > \angle B$, then $\sin A > \sin B$.
$(4)$ If the proposition "$p \land q$" is false, then $p$ and $q$ are both false propositions.
Identify the true proposition(s) among them. (Write down the number(s) of all true propositions)

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