
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 factory has two production lines, A and B. Before production line B was put into operation, production line A had already produced 200 tons of finished products. Starting from the operation of production line B, production lines A and B produce 20 tons and 30 tons of finished products per day, respectively.  
(1) Find the function relationship between the total output $y$ (in tons) of production lines A and B after B starts operation and the time $x$ (in days) since the start of B's operation;  
(2) Determine on which day, by the end of it, the total output of production lines A and B will be the same.

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