
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
Among the following propositions, identify the true ones (Fill in the corresponding numbers in front of the true propositions).

① Given two planes $\alpha$ and $\beta$, and two lines $a$ and $b$, if $\alpha \cap \beta = a$, $b \subset \alpha$, and $a \perp b$, then $\alpha \perp \beta$.

② Given two planes $\alpha$ and $\beta$, and two skew lines $a$ and $b$, if $a \subset \alpha$, $b \subset \beta$, $a \parallel \beta$, and $b \parallel \alpha$, then $\alpha \parallel \beta$.

③ Given three planes $\alpha$, $\beta$, and $\gamma$, and a line $l$, if $\alpha \perp \gamma$, $\beta \perp \gamma$, and $\alpha \cap \beta = l$, then $l \perp \gamma$.

④ Given two planes $\alpha$ and $\beta$, and a line $a$, if $\alpha \perp \beta$ and $a \perp \beta$, then $a \subset \alpha$ or $a \parallel \alpha$.

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