
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
Let $l, m, n$ be three distinct lines and let $\alpha, \beta, \gamma$ be three distinct planes. Let $A$ be a point. Consider the following statements: 
① If $l \parallel \alpha$ and $l \parallel m$, then $m \parallel \alpha$;  
② If $l \subset \alpha$, $m \cap \alpha = \{A\}$, and $A \notin l$, then $l$ and $m$ must be skew lines;  
③ If $l \subset \alpha$, $m \subset \beta$, $l \parallel \beta$, $m \parallel \alpha$, and $l$ and $m$ are skew lines, then $\alpha \parallel \beta$;  
④ If $\alpha \perp \beta$ and $l \subset \alpha$, then $l \perp \beta$;  
⑤ If $\alpha \cap \beta = l$, $\beta \cap \gamma = m$, $\gamma \cap \alpha = n$, and $l \parallel \gamma$, then $m \parallel n$.  
Identify all correct propositions.

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