
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]


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Three spheres, among which there are two identical ones, are tangent to the plane \( P \) and additionally touch each other pairwise. The vertex of a right circular cone lies on plane \( P \), and the axis of the cone is perpendicular to this plane. All three spheres are located outside the cone, and each of them touches its lateral surface. Find the cosine of the angle between a generator of the cone and plane \( P \), given that in the triangle formed by points of tangency of the spheres with the plane, one of the angles is \( 150^\circ \).

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