
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]


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(Solving application problems with equations) In order to win the battle for blue sky protection and build a charming and harmonious Changsha, the Changsha Environmental Protection Bureau carried out the renovation of a 2400-meter section of the Xiangjiang River. The renovation task was to be completed by two engineering teams, Team A and Team B. It is known that Team A can complete 30 meters per day, and Team B can complete 50 meters per day.  
$(1)$ If the task of renovating this section of the river is completed by Teams A and B working together, how many days will it take to complete the renovation?  
$(2)$ If Team A first works alone for a period of time before leaving, and the remaining work is completed by Team B in a total of 60 days, what lengths of the river were renovated by Team A and Team B respectively?

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