
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 the sphere, a diameter \(AB\) and two equal chords \(AM\) and \(AN\) are drawn, each positioned at an angle \(\alpha\) to the diameter. Find the angle between the chords if the segment \(MN\) is visible from the center of the sphere at an angle \(\beta\).

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