
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
Find the area of the surface part:
1) of the cone \( z^{2}=2xy \), located in the first octant between the planes \( x=2 \) and \( y=4 \);
2) of the sphere \( x^{2}+y^{2}+z^{2}=R^{2} \), located inside the cylinder \( x^{2}+y^{2}=Rx \);
3) of the cylinder \( x^{2}+y^{2}=Rx \), located inside the sphere \( x^{2}+y^{2}+z^{2}=R^{2} \).

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