
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]


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In order to cultivate students' habit of loving books, a certain school allocated some funds to purchase books. It is known that the school spent $5000$ yuan on buying books in the year $2020$, and $7200$ yuan in the year $2022$. Find the average annual growth rate of book purchasing funds from $2020$ to $2022$.

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