
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 the following four propositions:<br/>① If a line is perpendicular to two lines in a plane, then the line is perpendicular to the plane;<br/>② If a line is perpendicular to any line in a plane, then the line is perpendicular to the plane;<br/>③ If a line is perpendicular to the lines containing the two legs of a trapezoid, then the line is perpendicular to the lines containing the two bases of the trapezoid;<br/>④ If a line is perpendicular to the lines containing the two bases of a trapezoid, then the line is perpendicular to the lines containing the two legs of the trapezoid.<br/>The number of correct propositions is ______.

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