
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 the sequence \(\left\{a_{n}\right\}\) where \(a_{1}=7\) and \(\frac{a_{n+1}}{a_{n}}=a_{n}+2\) for \(n=1,2,3,\cdots\), find the smallest positive integer \(n\) such that \(a_{n}>4^{2018}\).

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