
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 $m$ and $n$ represent two non-coincident lines, and $\alpha$ represents a plane, determine the number of correct propositions among the following: $m \parallel n$, $m \bot \alpha \Rightarrow n \bot \alpha$, $m \bot \alpha$, $n \bot \alpha \Rightarrow m \parallel n$, $m \bot \alpha$, $n \parallel \alpha \Rightarrow m \bot n$, $m \parallel \alpha$, $m \bot n \Rightarrow n \bot \alpha$.

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