
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
The major axis of the ellipse $\dfrac {x^{2}}{16}+ \dfrac {y^{2}}{12}=1$ is $A_{1}A_{2}$, and the minor axis is $B_{1}B_{2}$. If the ellipse is folded along the $y$-axis to form a dihedral angle such that the projection of point $A_{1}$ on the plane $B_{1}A_{2}B_{2}$ is exactly the right focus of the ellipse, determine the size of this dihedral angle.

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