
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
Let $l_1$ and $l_2$ represent two lines, and $\alpha$ represent a plane. If we have ① $l_1 \perp l_2$; ② $l_1 \perp \alpha$; ③ $l_2 \subset \alpha$, then among all propositions that can be constructed by taking two of these as conditions and the other as the conclusion, the number of correct propositions is.

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