
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
To promote rural revitalization, the government vigorously supports small businesses. According to market demand, a small enterprise needs to update its production equipment to accelerate production speed. After updating the equipment, the production efficiency is increased by $25\%$. Before the update, the enterprise produced $x$ products per day. Answer the following questions:<br/>$(1)$ The number of products produced per day after the update is ______ (expressed in terms of $x$);<br/>$(2)$ If producing 5000 products before the update takes 2 days longer than producing 6000 products after the update, find how many products are produced per day after the update.

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