
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 planes $\alpha$, $\beta$, $\gamma$, and lines $l$, $m$ satisfying: $\alpha \perp \gamma$, $\gamma \cap \alpha = m$, $\gamma \cap \beta = l$, $l \perp m$, then the conclusions that can be drawn are: ① $m \perp \beta$; ② $l \perp \alpha$; ③ $\beta \perp \gamma$; ④ $\alpha \perp \beta$.  
Fill in the correct conclusion numbers.

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