
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 unit designs a mathematical model for the number of people $(n∈N^{+})$ to work with Shanghai Disneyland: The number of people entering the park in the $n$th time is represented by $f(n)= \begin{cases}200n+2000,n∈[1,8] \\ 360\cdot 3^{ \frac {n-8}{12}}+3000,n∈[9,32] \\ 32400-720n,n∈[33,45]\end{cases}$, and the number of people leaving the park in the $n$th time is represented by $g(n)= \begin{cases}0,n[1,18] \\ 500n-9000,n∈[19,32] \\ 8800,n∈[33,45]\end{cases}$. One computation unit is set as $15$ minutes, with $9$:$15$ AM as the first unit $(n=1)$, $9$:$30$ AM as the second unit $(n=2)$, and so on, dividing the day from $9$:$00$ AM to $8$:$15$ PM into $45$ computation units.

(1) Calculate the number of visitors entering and leaving the park between $2$:$00$ PM and $3$:$00$ PM, i.e., $f(21)+f(22)+f(23)+f(24)$ and $g(21)+g(22)+g(23)+g(24)$.

(2) If the park implements crowd control measures when the number of visitors reaches or exceeds $80,000$, will these measures be taken on that day at $4$:$00$ PM $(n=28)$? Explain your reasons.

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