
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
In space, there are \( n \) (\( n \geqslant 3 \)) planes, where any three planes do not share a common perpendicular plane. There are the following four assertions:
(1) No two planes are parallel to each other;
(2) No three planes intersect in a single line;
(3) Any two intersection lines between the planes are not parallel;
(4) Each intersection line between the planes intersects with \( n-2 \) other planes.

Determine how many of these assertions are correct.

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