
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
There are four propositions concerning line $m$, line $n$, plane $a$, and plane $b$:
1. If $m \parallel a$, $n \parallel b$, and $a \parallel b$, then $m \parallel n$.
2. If $m \parallel n$, $m$ is contained in $a$, and $n$ is perpendicular to $b$, then $a$ is perpendicular to $b$.
3. When $a$ intersects $b$ at $m$, and $m \parallel n$, then $n \parallel a$ and $n \parallel b$.
4. If $m$ is perpendicular to $n$, and $a$ intersects $b$ at $m$, then $n$ is perpendicular to either $a$ or $b$.

The propositions that are false are numbered:

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