
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 certain school is renovating and maintaining the track and field during the summer vacation. The project contracting unit dispatched the first construction team to start the construction work, planning to complete the entire project in 30 days. After working for 10 days, the contracting unit received a notice that a large event was scheduled to be held at the track and field. They were required to complete the entire project 8 days earlier than originally planned. Therefore, the contracting unit dispatched the second construction team to work together with the first team to complete the remaining work, and the entire project was completed on time as requested.  
$(1)$ If the second construction team works alone, how many days will it take to complete the entire project?  
$(2)$ If both the first and second construction teams work together on this project, how many days will it take to complete the entire project?

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