
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
In a plane, there is a line $y$ and a right triangle $A B C$ with legs $A C = 3$ and $B C = 4$. The vertex $C$ is at a distance of 10 from the line $y$. The angle between $y$ and the direction of leg $A C$ is $\alpha$. Determine the angle $\alpha$ that minimizes the surface area obtained by rotating triangle $A B C$ around the line $y$.

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