
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 \(a\) is a natural number, and there is a quadratic trinomial with integer coefficients using \(a\) as the leading coefficient that has two distinct positive roots less than 1. Find the smallest value of \(a\).

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