
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 following four propositions:
1. The negation of the proposition "For all $x \in \mathbb{R}$, $\cos x > 0$" is "There exists an $x \in \mathbb{R}$ such that $\cos x \leqslant 0$".
2. The necessary and sufficient condition for three lines $a$, $b$, and $c$ in space to satisfy $a \| b$ is that $a \perp c$ and $b \perp c$.
3. In $\triangle ABC$, if the proposition "If $A > B$, then $\sin A > \sin B$" is true, then its converse is false.
4. Some vectors have coordinates equal to the coordinates of their initial points. Identify the valid propositions (Provide the numbers of all true propositions).

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