
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
The decimal representation of the four-digit number АБВГ, consisting of distinct digits, is divided into three parts in three ways, resulting in three quadratic equations:

1. \( \mathrm{A} x^{2} + Б x + \mathrm{B} \Gamma = 0 \)
2. \( \mathrm{A} x^{2} + \mathrm{Б} \mathrm{B} x + \Gamma = 0 \)
3. \( \mathrm{A} x^{2} + \mathrm{B} x + \Gamma = 0 \).

It turns out that all these equations have roots. Find all possible values of АБВГ.

Here, АБ, БВ, and ВГ are not products of digits, but two-digit numbers. In both the representation of АБВГ and these two-digit numbers, the first digits cannot be equal to 0.

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