
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
There are two fitness centers, A and B. Both have similar equipment and services, but their pricing methods differ. Center A charges 5 yuan per hour, while Center B charges 90 yuan per month for up to 30 hours (including 30 hours), and 2 yuan per hour for any time exceeding 30 hours. A person plans to choose one of these two centers for fitness activities next month, with their activity time being no less than 15 hours and no more than 40 hours.

1. Let f(x) represent the cost (in yuan) of exercising for x hours (15 ≤ x ≤ 40) at Center A, and g(x) represent the cost at Center B. Find f(x) and g(x).
2. Which center is more cost-effective? Why?

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