
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
The government plans to build a road of $1000$ meters long for a certain village, with two construction teams, Team A and Team B, responsible for the construction. It is known that if Team A works independently for $5$ days, Team B joins in, and after working together for $8$ days, there are still $30$ meters of work left. Team A working for $2$ days completes $20$ meters less work than Team B working for $3$ days. <br/>$(1)$ Find out how many meters each team constructs per day. <br/>$(2)$ Now, it is planned for the two teams to work together to complete the project. After working together for $4$ days, Team A has to leave due to some reason, and the remaining work is completed independently by Team B. If the project needs to be completed within $12$ days, how many more meters should Team B construct per day at least?

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