
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 $a$, $b$, $c$ be three distinct lines, and $\alpha$, $\beta$, $\gamma$ be three distinct planes. Consider the following propositions:
1. If $\alpha \perp \gamma$ and $\beta \perp \gamma$, then $\alpha \parallel \beta$;
2. If lines $a$ and $b$ are skew, $a \subset \alpha$, $b \subset \beta$, $a \parallel \beta$, and $b \parallel \alpha$, then $\alpha \parallel \beta$;
3. If $\alpha \cap \beta = a$, $\varnothing \cap \gamma = b$, $\gamma \cap a = c$, and $a \parallel b$, then $c \parallel \beta$;
4. If $a$ and $b$ are skew lines, $a \parallel \alpha$, $b \parallel \alpha$, $c \perp a$, and $c \perp b$, then $c \perp \alpha$.

Among these propositions, the correct ones are.

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