
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
Consider the polynomial equation \[x^3 + dx + e = 0,\] where $d$ and $e$ are rational numbers, and one of its roots is $2-\sqrt{5}$. The polynomial also has another root which is an integer. What is that root?

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