
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 telecom company offers two billing plans for mobile phone usage. Plan A has a fixed monthly rental of 50 yuan, regardless of the call duration, plus a charge of 0.4 yuan per minute of call. Plan B has no monthly rental, but charges 0.6 yuan per minute of call.  
(1) If the monthly fees for Plan A and Plan B are denoted as $y_1$ yuan and $y_2$ yuan respectively, write the relationship between the monthly fee $y$ (in yuan) and the call duration $x$ (in minutes);  
(2) If the average monthly call duration is 300 minutes, which plan would you choose?  
(3) How many minutes of calls per month would result in the same charges for Plan A and Plan B?

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