
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 that \(a_{1}, a_{2}, a_{3}, \cdots, a_{n}\) are natural numbers satisfying \(0<a_{1}<a_{2}<a_{3}< \cdots <a_{n}\) and \(\frac{13}{14} = \frac{1}{a_{1}} + \frac{1}{a_{2}} + \frac{1}{a_{3}} + \cdots + \frac{1}{a_{n}}\), find the smallest value of \(n\).

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