
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
Among the following propositions:<br/>① Two lines intersected by a third line have equal corresponding angles;<br/>② There is only one line passing through a point that is parallel to a given line;<br/>③ If $\angle 1 = 40^{\circ}$ and the two sides of $\angle 2$ are parallel to the two sides of $\angle 1$, then $\angle 2 = 40^{\circ}$ or $140^{\circ}$;<br/>④ If $b\bot c$ and $a\bot c$, then $b$ is parallel to $a$. The false propositions are______ (Fill in the numbers).

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