
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 positive integer \(a\), there exists a quadratic trinomial with integer coefficients, where \(a\) is the coefficient of the quadratic term, and it has two distinct positive roots both less than 1. Find the smallest value of \(a\).

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