
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 two perpendicular planes, consider the following statements:
① A line in one plane must be perpendicular to any line in the other plane;
② A line in one plane must be perpendicular to countless lines in the other plane;
③ Any line in one plane must be perpendicular to the other plane;
④ If a perpendicular to the intersection line is drawn from any point in one plane, then this perpendicular must be perpendicular to the other plane.
The correct statements in order are.

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