
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
Make a cylindrical grain storage with a flat bottom and a conical cover out of tinplate. The volume of the grain storage (excluding the space inside the conical cover) is $(8+8\sqrt{2})\pi \text{m}^3$. The angle between the slant height of the cover and the radius of the base circle is 45°. Let the radius of the base circle of the grain storage be $R$ meters, and the area of the tinplate required be denoted as $S(R)$ square meters (joints, etc., are not considered).  
(1) Express $S(R)$ as a function of $R$;  
(2) Find the minimum value of $S(R)$ and the total height of the grain storage (including the conical cover).

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