
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 general term of the sequence \( 101, 104, 109, 116, \cdots \) is \( a_{n}=100+n^{n} \), where \( n=1,2,3, \cdots \). For each \( n \), \( d_{n} \) represents the greatest common divisor (GCD) of \( a_{n} \) and \( a_{n-1} \). What is the maximum value of \( d_{n} \)?

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