
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 a line $l$, a line $m$, a plane $\alpha$, and a plane $\beta$ with the conditions $l \perpendicular \alpha$ and $m \subset \beta$. Consider the following four propositions:  
① If $\alpha \parallel \beta$, then $l \perpendicular m$;  
② If $l \perpendicular m$, then $\alpha \parallel \beta$;  
③ If $\alpha \perpendicular \beta$, then $l \parallel m$;  
④ If $l \parallel m$, then $\alpha \perpendicular \beta$.  
The number of true propositions is \_\_\_\_\_\_\_\_.

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