
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
A shared bicycle operation company is preparing to purchase a batch of shared bicycles to enter the market. However, the shared bicycle installation company is unable to allocate enough skilled workers and is preparing to recruit a group of new workers. It is known that 2 skilled workers and 3 new workers can install a total of 44 shared bicycles per day; 4 skilled workers install the same number of shared bicycles per day as 5 new workers.

$(1)$ Find out how many shared bicycles each skilled worker and new worker can install per day.

$(2)$ The shared bicycle installation company plans to allocate a certain number of skilled workers and recruit new workers to install shared bicycles together. If exactly 3500 qualified bicycles are delivered to the operation company after 25 days, find out how many skilled workers and new workers there are.

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