
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
Three different lines, $\alpha$, $\beta$, $\gamma$ are three different planes:  
① If $\alpha \perp \beta$, $\beta \perp \gamma$, then $\alpha \parallel \beta$;  
② If $a \perp b$, $b \perp c$, then $a \parallel c$ or $a \perp c$;  
③ If $a \subset \alpha$, $b, c \subset \beta$, $a \perp b$, $a \perp c$, then $\alpha \perp \beta$;  
④ If $a \perp \alpha$, $b \subset \beta$, $a \parallel b$, then $\alpha \perp \beta$, among the above four propositions, the number of true propositions is.

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