
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

Three equal cones with an apex angle $\alpha$ $(\alpha \leqslant \frac{2 \pi}{3})$ in the axial section have a common vertex and touch each other externally along the generators $k, l, m$. Find the angle between the generators $l$ and $k$.

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