
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
Positive integer \(a\) and integers \(b\) and \(c\), in the three-dimensional coordinate system \(O-xyz\), point \(O(0,0,0)\), \(A(a, b, c)\), and \(B\left(x^{2}, x, 1\right)\) satisfy that the angle between \(\overrightarrow{OA}\) and \(\overrightarrow{OB}\) is \(\frac{\pi}{2}\). Given that the real number \(x\) has exactly two distinct solutions \( x_{1} \) and \( x_{2} \) in the interval \((0,1)\), find the minimum value of \(a\).

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