
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
A plane intersects the faces and the edge of a dihedral angle, such that the projection of the edge onto this plane coincides with the angle bisector formed by the intersection of the plane with the dihedral angle. The edge forms an angle of $\alpha$ with the plane, and the angle formed in the intersection is $\beta$. Find the measure of the dihedral angle.

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