
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
Solve the equations \(2x^3 - 5x^2 + 6x - 2 = 0\) and \(6x^3 - 3x^2 - 2x + 1 = 0\), given that they have a common root.

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