
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
In 2019, our county built 4 million square meters of new housing, of which 2.5 million square meters are mid-to-low-priced houses. It is expected that in the coming years, the average annual increase in the area of new housing in our county will be 8% higher than the previous year. In addition, the area of mid-to-low-priced houses built each year will increase by 500,000 square meters compared to the previous year. So, by the end of which year:<br/>
$(1)$ The cumulative area of mid-to-low-priced houses built in our county over the years (with 2019 as the first cumulative year) will first exceed 22.5 million square meters?<br/>
$(2)$ The proportion of the area of mid-to-low-priced houses built in that year to the total area of housing built in that year will first exceed 85%? (Reference data: $1.08^{4}\approx 1.36$, $1.08^{5}\approx 1.47$)

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