
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
Typhoon "Dusu Ray" has touched the hearts of the people across the country. A certain unit has launched a disaster relief donation activity with the theme "When one place is in trouble, support comes from all directions." On the first day, they received a donation of $3000$, and on the third day, they received a donation of $4320$.  
$(1)$ If the donation growth rates on the second and third days are the same, find the donation growth rate.  
$(2)$ Based on the donation growth rate calculated in $(1)$, how much donation can the unit receive on the fourth day?

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