
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 lines $a$, $b$ and plane $\alpha$ that satisfy: ①$a$ is parallel to $b$, ②$a$ is perpendicular to $\alpha$, ③$b$ is perpendicular to $\alpha$, if two of these conditions are chosen as premises and the remaining one as a conclusion, the number of true propositions that can be obtained is $\_\_\_\_\_\_$.

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