
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 mathematical model is designed to determine the number of people $(n∈N^{+})$ for a unit working with Shanghai Disneyland. The model represents the number of people entering the park in the $n^{th}$ time with $f(n)= \begin{cases} 200n+2000,n∈[1,8] \\\\ 360⋅ 3^{ \frac {n-8}{12}}+3000,n∈[9,32] \\\\ 32400-720n,n∈[33,45]\end{cases}$ and the number of people leaving the park in the $n^{th}$ moment with $g(n)= \begin{cases} 0,n[1,18] \\\\ 500n-9000,n∈[19,32] \\\\ 8800,n∈[33,45]\end{cases}$. Setting every $15$ minutes as a computing unit, starting from 9:15 am as the first unit $(n=1)$, 9:30 am as the second unit $(n=2)$, and so on, until 8:15 pm, which is divided into 45 computing units in total. (The final result is rounded, accurate to an integer).

(1) Calculate the number of people entering the park $f(21)+f(22)+f(23)+f(24)$ and leaving the park $g(21)+g(22)+g(23)+g(24)$ between 2 pm and 3 pm?

(2) Starting from 1:45 pm $(n=19)$, there are visitors leaving the park. Please find the time when the park has the most visitors and explain the reason.

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