
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
Let \( a \) and \( n \) be natural numbers, and it is known that \( a^{n} \) is a 2014-digit number. Find the smallest natural \( k \) such that \( a \) cannot be a \( k \)-digit number.

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