
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
There are three propositions:
1. Two lines perpendicular to the same plane are parallel;
2. A skew line $l$ through plane $\alpha$ has only one plane perpendicular to $\alpha$;
3. If skew lines $a$ and $b$ are not perpendicular, then any plane passing through $a$ is not perpendicular to $b$. The number of correct propositions is

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