
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
Find the smallest positive integer \( a \) such that for some integers \( b \) and \( c \), the polynomial \( ax^2 - bx + c \) has two distinct zeros in the interval \( (0, 1) \).

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