
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 original area of a forest was $a$. It was planned to cut down some trees each year such that the forest area reduced by $p\%$ each year. After 10 years, the forest area became $\frac {a}{2}$. To protect the ecological environment, the forest area needs to be maintained at at least $\frac {1}{4}$ of the original area. It is known that up to this year, the forest area is $\frac { \sqrt {2}}{2}a$.  
(1) Find the value of $p\%$.  
(2) Until this year, how many years have the trees been cut down?  
(3) How many more years can trees still be cut down at most?

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