
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 polynomial equation \[x^4 + ax^2 + bx + c = 0,\]where $a, b,$ and $c$ are rational numbers, has $2-\sqrt{5}$ as a root. It also has two integer roots. What are they?

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