
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 three different planes $\alpha$, $\beta$, $\gamma$, and lines $a$, $b$, $c$ respectively in planes $\alpha$, $\beta$, $\gamma$. If $\beta \perp \gamma$ and $\alpha$ intersects $\gamma$ but not perpendicularly, then which of the following statements are true?  
① $\forall b \subset \beta$, $b \perp \gamma$     ② $\forall b \subset \beta$, $b \parallel \gamma$    ③ $\exists a \subset \alpha$, $a \perp \gamma$  
④ $\exists a \subset \alpha$, $a \parallel \gamma$     ⑤ $\forall c \subset \gamma$, $c \parallel \alpha$    ⑥ $\exists c \subset \gamma$, $c \perp \beta$

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