
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 that the angle between skew lines \(a\) and \(b\) is \(60^{\circ}\), and from a point \(P\) in space, a line \(l\) is constructed to form an angle \(\alpha\) (where \(0^{\circ} < \alpha < 90^{\circ}\)) with both \(a\) and \(b\), determine \(f(\alpha)\), the number of such lines \(l\).

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