
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 half-planes $\alpha_{1}, \alpha_{2}, \ldots, \alpha_{n}$ share a common edge $l$. What is the sum of the dihedral angles $\alpha_{1} \widehat{l \alpha_{2}}, \alpha_{2} \widehat{l \alpha_{3}}, \ldots, \alpha_{n-1} \widehat{l \alpha_{n}}$, $\alpha_{n} \widehat{l \alpha_{1}}$, that together span the entire space?

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