
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 skew lines $a$ and $b$ forming an angle of $80^\circ$, and a fixed point $P$ not on lines $a$ or $b$. If there are exactly two lines passing through $P$ that form equal angles with lines $a$ and $b$, and these angles are equal to $\alpha$, determine the set to which angle $\alpha$ belongs.

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