
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 that $m$ and $n$ are two lines outside of plane $\alpha$, their projections within plane $\alpha$ are lines $m_1$ and $n_1$ respectively. Among the following four propositions: ①$m_1$∥$n_1$⇒$m$∥$n$; ②$m$∥$n$⇒$m_1$ and $n_1$ are parallel or coincident; ③$m_1$⊥$n_1$⇒$m$⊥$n$; ④$m$⊥$n$⇒$m_1$⊥$n_1$. Identify the sequence numbers of all false propositions.

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