
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
The saxaul tree is known as the "king of desert vegetation" due to its tenacious vitality and its role in wind prevention and sand fixation. In a desert in northern Xinjiang, there were 160,000 mu of saxaul trees in the year 2021. After two years of artificial planting and natural reproduction, the area reached 250,000 mu in 2023.
- $(1)$ Find the average annual growth rate over these two years.
- $(2)$ Estimate the area of saxaul trees in this desert in the year 2024.

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