
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
If \(\alpha\) is a real root of the equation \(x^{5}-x^{3}+x-2=0\), find the value of \(\left\lfloor\alpha^{6}\right\rfloor\), where \(\lfloor x\rfloor\) is the greatest integer less than or equal to \(x\).

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