
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
An underground pipeline can be laid by Team A alone in 12 days, and by Team B alone in 24 days. <br/> $(1)$ If these two teams work simultaneously from both ends, how many days will it take to lay the pipeline?<br/> $(2)$ If Team A and Team B cooperate for the first $(a+3)$ days, and the remaining work is completed by Team A in $(4a+2)$ days, exactly finishing the project, how many days in total did Team A participate?

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