
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
(This question is worth a total of 12 points) A store plans to purchase 36 desks worth 20 yuan each in batches within a month. Each batch will purchase $x$ desks ($x$ is a positive integer), and each batch will incur a shipping fee of 4 yuan. The storage fee for storing the purchased desks for a month is directly proportional to the total value of the desks purchased per batch (excluding shipping fees). If 4 desks are purchased per batch, the total cost for shipping and storage fees for the month will be 52 yuan. Now, there are only 48 yuan available for the month to cover shipping and storage fees.  
(I) Calculate the total cost $f(x)$ of shipping and storage fees for the month;  
(II) Is it possible to properly arrange the number of desks purchased per batch so that the funds are sufficient? Write your conclusion and explain your reasoning.

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