
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 that line \\(l\\) is perpendicular to plane \\(\alpha\\), and line \\(m\\) is contained in plane \\(\beta\\), consider the following three propositions: \\(① \alpha \parallel \beta \Rightarrow l \perp m; ② \alpha \perp \beta \Rightarrow l \parallel m; ③ l \parallel m \Rightarrow \alpha \perp \beta.\\) The number of true propositions is \_\_\_\_.

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