
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
Regarding the projection of right angle $AOB$ within a fixed plane $\alpha$, the following judgments are made: $(1)$ It could be a $0^{\circ}$ angle; $(2)$ It could be an acute angle; $(3)$ It could be a right angle; $(4)$ It could be an obtuse angle; $(5)$ It could be a $180^{\circ}$ angle. Among these, the correct judgments are __________. (Note: Fill in all the numbers you think are correct).

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