
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
Given \( n \) is an integer greater than 2, let \( a_{n} \) be the largest \( n \)-digit number that is neither the sum of two perfect squares nor the difference of two perfect squares.
1. Find \( a_{n} \) (expressed as a function of \( n \)).
2. Find the smallest value of \( n \) such that the sum of the squares of the digits of \( n \) is a perfect square.

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