
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:<br/>$p_{1}$: Three lines that intersect pairwise and do not pass through the same point must lie in the same plane.<br/>$p_{2}$: Any three points in space determine one and only one plane.<br/>$p_{3}$: If two lines in space do not intersect, then they are parallel.<br/>$p_{4}$: If line $l$ is contained in plane $\alpha$, and line $m$ is perpendicular to plane $\alpha$, then $m$ is perpendicular to $l$.<br/>Among the following propositions, the numbers of all true propositions are ____.<br/>①$p_{1}\wedge p_{4}$<br/>②$p_{1}\wedge p_{2}$<br/>③￢$p_{2}\vee p_{3}$<br/>④￢$p_{3}\vee $￢$p_{4}$

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