
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 a certain region, the initial stock of timber in the forest was $a$, and it grows at an annual rate of 25%. Due to the need for production and construction, the volume of timber harvested at the end of each year is $b$. Let $a_n$ be the stock of timber in the forest after $n$ years,

(1) Express $a_1$, $a_2$, $a_3$;  
(2) Find the expression for $a_n$;  
(3) To protect the ecological environment and prevent soil erosion, the timber stock in this area should not be less than $\frac{7}{9}a$ each year. If $b=\frac{19a}{72}$, will there be soil erosion in this area in the future? If so, how many years will it take? (Reference data: $\lg 2=0.3$)

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