
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 sequence \(\{a_n\}\) is defined by the recurrence relation:
\[ a_1 = 1, \quad a_{n+1} = a_n + \frac{1}{a_n}, \quad n \geq 1. \]

Find all \( n \) such that \( a_n > 20 \).
(18th All-Russian Mathematical Olympiad, 1992)

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