
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
设甲设备生产的产品数量为$x$件，乙设备生产的数量为$4800-x$件。根据分层抽样的原则，样本中甲设备生产的产品数量与乙设备生产的产品数量应与总体中它们的比例相同。即，
$$ \frac{\text{样本中甲设备的产品数量}}{\text{总样本数量}} = \frac{x}{4800} $$
根据题目中的数据，我们知道样本中甲设备生产的产品数量是50，总样本数量是80。因此，
$$ \frac{50}{80} = \frac{x}{4800} $$

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