
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 a sequence of natural numbers \( a_n \) whose terms satisfy the relation \( a_{n+1}=k \cdot \frac{a_n}{a_{n-1}} \) (for \( n \geq 2 \)). All terms of the sequence are integers. It is known that \( a_1=1 \) and \( a_{2018}=2020 \). Find the smallest natural \( k \) for which this is possible.

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