
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 sum of all roots of the equation:

$$
\begin{gathered}
\sqrt{2 x^{2}-2024 x+1023131} + \sqrt{3 x^{2}-2025 x+1023132} + \sqrt{4 x^{2}-2026 x+1023133} = \\
= \sqrt{x^{2}-x+1} + \sqrt{2 x^{2}-2 x+2} + \sqrt{3 x^{2}-3 x+3}
\end{gathered}
$$

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