
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
Calculate the surface areas of:

a) The cylinder \(x^{2} + y^{2} = R^{2}\) bounded by the planes \(z = 0\) and \(z - y = 0\).

b) The cylinder \(y^{2} + z^{2} = R^{2}\) with \(z \geqslant 0\), bounded inside the cylinder \(x^{2} + y^{2} = R^{2}\).

c) The paraboloid \(x^{2} + y^{2} = 6z\) bounded inside the cylinder \(x^{2} + y^{2} = 27\).

d) The sphere \(x^{2} + y^{2} + z^{2} = 3a^{2}\) bounded inside the paraboloid \(x^{2} + y^{2} = 2az\), where \(a > 0\).

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