
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
For \( n=1,2,3, \ldots \), let \( a_{n}=n^{2}+100 \), and let \( d_{n} \) denote the greatest common divisor of \( a_{n} \) and \( a_{n+1} \). Find the maximum value of \( d_{n} \) as \( n \) ranges over all positive integers.

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