
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
(5 points) Let $l$ be a line, and $\alpha$, $\beta$, $\gamma$ be three distinct planes. Consider the following four propositions: ① If $\alpha \perp \gamma$ and $\beta \perp \gamma$, then $\alpha \perp \beta$; ② If $\alpha \perp \gamma$ and $\beta \parallel \gamma$, then $\alpha \perp \beta$; ③ If $l \parallel \alpha$ and $l \perp \beta$, then $\alpha \perp \beta$; ④ If $l \parallel \alpha$, then $l$ is parallel to all lines within $\alpha$. The correct propositions are  
        . (Fill in the numbers of all propositions you believe are correct)

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